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THE NEW YORK 

POBUC LIBRARY 







Q 

O 
it 

O 



S 



I 



r 



WATER POWER ENGINEERING 



THE THEORY. INVESTIGATION AND DEVELOPMENT 
OF WATER POWERS. 



BY 

Daniel w. mead. 

Member American Society Civil Enginan 

Consul/ f fig" Engineer 

Professor of Hydraulic and Sanitary Engineering 

University of Wisconsin 



First E'lition. 



NEW YORK 

McGraw-Hill Book Co, 
19O8 



THE NEW YORK 

PUBLIC LIBRARY 

63248^ 

•iTO« LC«tUR AMD 



Copyrighted 1907-1908 

BY 

Daniel W. Mead 



:': ••• •. .• 



*• •*•*! •*. 



Btatm JouaiTAL yRonam CourAgrt 
Ma»i«on, WiaooMnr 



PREFACE 



In the development of a water power project the engineer is fre- 
qently called upon to do more than design and construct the power 
plant. He may be required to report on.the adequacy of the supply, 
the head and power available and the probable variations in the 
same, the plan for development, the cost of construction and opera- 
tion, and the advisability of the investment. A study of the entire 
project, therefore, becomes essential, and each factor must be care- 
fully considered in detail to assure ultimate success. Each of the 
features of the development is of equal importance to the commer- 
cial success of the project. The majority of the failures in water 
power development have occurred from causes other than structural 
defects, and a knowledge of these other important and controlling 
factors is therefore quite as essential as a knowledge of design and 
construction. It must be said, however, that in respect to some of 
these controlling factors current practice has not been what it should 
l>e. This has resulted in many over-developments and illy advised 
installations, from which the power generated has not been equal 
to that anticipated, and in many poor financial investments amount- 
ing frequently to practical failures. The engineer has given much 
attention to design and construction but too little attention to the 
other fundamental considerations mentioned above on which the 
success of the project depends to an equal extent. 

In the preparation of this book the author has endeavored to con- 
sider, briefly at least, all fundamental principles and to point out the 
basis on which successful .^'Mer power-, cqvelopment depends. The 
method of study and inyestig^tipn outlined herein was developed by 
the author during tweuty^five year'$ of professional practice and in 
his efforts to illustrate the. principles underlying the subject in his 
lectures to the senior ^•class^iji.wateJ*. power engineering at the Uni- 
versity of Wisconsin. A somewhat extended acquaintance with the 
literature relating to water power engineering leads the author to 
believe that in a number of features the principles and methods de- 
scribed in this book are ^mewhat in advance of present practice. 



VI 



Preface, 



In current practice, the hydraulic engineer, to determine the ex- 
tent of a proposed hydraulic development, commonly depends on a 
study of the monthly averages of stream flow and of observed maxi- 
mum and minimum Oows. He usually assumes from his previous 
knowledge and study that the development should be based on a 
certain minimum or average stream discharge per square mile of 
drainage area. The value of this method depends on the breadth of 
the engineer's local knowledge of rainfall and run-oflf relations. 
With a sufficient knowledge of these conditions, this method may 
form a safe basis for water power development but it fails to give 
the complete information which is essential for a full comprehension 
of the subject. In other cases the development is predicted on a 
single, or on a very few, measurements of what is believed, or as- 
sumed to be, the low water flow of the stream. This method, evettfl 
when accompanied by careful study of rainfall records, is a danger* 
ous one to employ as many over-developed water power projects 
demonstrate. Neither of these methods compares favorably with 
the more exact method of studying flow by actual or comparative^ 
hydrographs as is described in Chaps. IV, V, VI 11 and IX. " 

In current practice the head available is usually determined for 
average conditions, or, perhaps, occasionally for low, average and 
high water conditions, and no detailed study of the daily e fleet on 
power is attempted* In Chaps. IV and V this subject is presented 
in detail and a method of the investigation of this important subject, 
under all conditions of flow and all conditions of use, is outlined. 

On the basis of the kno%vledge gained from the study of flow and 
head, the study of the power that can be developed for each day ini 
the year and during each year for which actual or comparative hy-J 
drographs are available, is outlined. An outline of a method for 
the consideration of possible variations in flow during periods for] 
which no measurements arc available based on the available rain-J 
fall records, is also given*, ii>f:haj]^,-VJ.:VM •and VIIL A study of 
the effect of pondage OTv'pfiier' k mc^tMmpc>rtant matter, though 
not always carefully considcrel^, pr ^{^J-er^sftcd, is also discussed in — 
considerable detail in Chaps. lV,:V^"na'^XxVl. | 

In the selection of turbines,4fi)j:a'\vs(6en power project* the current 
practice has been for the erfgtntir; Whilfe rtfawing certain conclu- 
sions from the tables of manufacturers' catalogues, to present to the 
manufacturer the conditions under which the power is to be devel-^ 
oped and to rely largely or entirely on the manufacturer for advice] 



Preface. vii 

as to machinery to be used. In such cases he is dependent for re- 
sults on guarantees which are usually quite indefinite in character 
and seldom verified by actual tests, under working conditions, be- 
fore the wheels are accepted and paid for. This has resulted in 
many cases in the installation of wheels which are entirely unsuited 
to the particular conditions under which they are installed. 

Practical turbine analysis has not been treated except in the most 
general way in any publications except the various German treatises 
on the turbine in which the subject is discussed from the basis of 
turbine design. The author has developed the method of turbine 
analysis and selection, outlined in Chapters XIV and XVI. 
which applies to all wheels when tests of wheels of the series or 
class considered are available. These methods are based on the 
practical operating conditions of actual tests and are both theoreti- 
cally and practically correct. The engineer should be able to intel- 
ligently select the turbines needed for the particular conditions of his 
installation and to determine, with a considerable degree of accuracy, 
the results on which he can depend during all conditions of head 
and flow. 

It is believed that this treatment of the subject is sufficiently 
complete to place the selection of turbines on a better footing and 
that, when adopted, it will lead to the selection of better and more 
improved designs and assure more satisfactory results. 

The subject of turbine governing has, for electrical reasons, be- 
come an important one. While a number of important papers have 
appeared on this subject, there is, so far as the author knows, no 
discussion in English which offers the engineer a basis for a com- 
plete consideration of this subject. Chap. XVIII, on the principles 
of turbine governing together with appendixes A, B and C, offer, 
it is believed, suggestions for the consideration of this subject which 
may prove of value to water power engineers. 

The report on a water power project should involve a careful 
and complete investigation of the entire subject, and should be 
based on the broadest considerations of the project in all its rela- 
tions. Many reports which have come to the author's attention 
bave been too limited in scope and have included only general opin- 
ions which have not. to his mind, been sufficiently specific or based 
on sufficient information to warrant approval without extended in- 
vestigations. In Chap. XXVIII the author has outlined his idea 



viii Preface. 

of the extent and scope of such investigation and report, which h 
believes is essential for an intelligent investigation and a reliabl 
opinion on this subject. 

ACKNOWLEDGMENTS. 

There can be little which is strictly new or original in any technics 
work, and in offering this book to the profession, the author wishes t 
acknowledge his indebtedness to the large number of technical ai 
tides that have already appeared on various phases of the subjecl 
Many references to such literature have been given at the end of th 
various chapters. 

Many illustrations have been taken, with more or less chang 
from Engineering News, Engineering Record, Cassier's Magazin 
and Electrical World and Engineer. Various manufacturers hav 
furnished photographs and, in some cases, cuts of their wheels, go\ 
ernors and apparatus, in connection with which their names appeal 

Tlie author has been greatly aided by his assistants, both of hi 
own private office and of the University staff. He wishes especiall 
to acknowledge the assistance of Mr. L. F. Harza to whoi 
Chap. XVIII on The Speed Regulation of Turbine Water Wheel 
and appendixes A, B and C are largely due. Mr. Harza has als 
been of much assistance in the editorial work of publication. Ej 
pecial acknowledgment is also due to Professor G. J. Davis, Ji 
for the preparation of the diagrams of friction of water in pipes an 
of Bazin's and Kutter's coefficients, etc. Mr. Robert Ewald assistc 
in the selection of material for illustrations, in the investigation < 
German literature, and the preparation of various graphical diagram 
including the first development of the characteristic curve. 

The author also desires to acknowledge his indebtedness to h 
principal assistant, Mr. C. V. Seastone, for advice and assistance i 
the arrangement of many of the chapters in this work and assis 
ance in the editorial work of publication. 

The sources of various other tables, illustrations, etc., are a 
knowledged in their proper places. D. W. M. 

Madison, Oct. i, 1908. 



CONTENTS 



CHAPTER I. 

Introduction. 

The Hwtory of Water Power Development— Every Development of 
Water Power — ^The EiarlieBt Type of Water Wheel — ^The Undershot 
Wheel — The Overshot and Breast Water Wheel — ^The Development 
of the Turhine— Fundamental Ideas of the Turhlne— The Modem 
Turhin&— The American or Francla Turbine — ^Modern Changes in 
Turbine Practice — Historical Notes on Water Power Development — 
Development of Water Power in the United States — ^Literature. ••• 1 

CHAPTER IL 
Power. 

The Development of Potential Energy — Definition of Energy — Solar 
Energy the Ultimate Source — ^No Waste of Energy in Nature— Laws 
of Energy Conservation — Efficiency — Natural Limit to Efficiency — • 
Practical Limits to Efficiency — Efficiency of a Combined Plant- 
Capacity of Each Part of a System not Identical — The Analysis of 
Losses — The Losses In a Hydro-Electric Plant— Units of Energy'— 
Conversion of Energy Units — ^Kinetic Energy — Uniform Motion — 
Uniform Varied Motion — Compound Motiour-Qraphlcal Representa- 
tion of the Laws of Motion — ^Transformation — ^Literature 19 

CHAPTER IIL 

Hydraulics. 

Basis of Hydraulics — Mathematical Expression for Energy— Velocity 
Head*— Entrance Head — Submerged Orifices — Friction Head — Kut- 
ter's Formula — Bazin's Formula — ^Efficiency of Section — ^Determina- 
tion of Canal Cross-Section — The Back Water Curve — Flow of 
Water in Pipes — The Flow of Water Through Orifices — Flow over 
Weirs — ^Literature 40 

CHAPTER IV. 

Wateb Powis. 

The Study of the Power of a Stream as Affected by Flow— Source of 
Water Power — Factors of Stream Flow — Broad Knowledge of 



Contents. 

Stream Plow Neceasary— The Hydrograph— The Use of Local 
Hydrography— Use of Comparative Hydrographs— Reliability of 
Comparauve Hydrographfl— When no Hydrographs are Available— 
The Hydrograph as a Power Curve 7S^ 



CHAPTER V. 

Wateb Poweb (Continued) 

The Study of the Power of a Stream as Affected by Head— Variations 
in Head — The Rating or Discharge Curve— The Tail Water Curve — 
The Head Water Curve— Graphic Representation of Head — Effects 
of Design of Dam on Head — Effect of Head on the Power of the 
Plant — Graphical Representation of the Relations of Power, Head 
and Plow — Graphical Study of Power at Kilbourn — Power of the 
Kilbourn Wheels Under Variations in Flow— Effects of Low Water 
Flow — Effects of Number of Wheels on Head and Power • 9 J 



CHAPTER VL 

Rainfall. 

Importance of Rainfall Study — Distribution of Rainfall — The Rainfall 
Must be Studied in Detail — ^Local Variation in Annual Rainfalls— 
Local Variations in Periodical Distribution of Annual Rainfall — 
. Accuracy of Rainfall Maps and Records — Rainfall and Altitude — 
Value of Extended Rainfall Records — Accuracy in Rainfall Obser- 
vation*— District Rainfall — Study of Rainfall as Affecting Run-off — 
Literature.. ..c 111- 



CHAPTER VII. 

The Disposal of the Rainfall. 

Pactors of Disposal — The Rate or Intensity of Rainfall— Condition of 
Receiving Surfaces and Geological Strata — Effects of Wind — Effects 
of Vegetation — Percolation— Evaporation — Evaporation Relations — 
Practical Consideration of Losses — Literature 133- 



CHAPTER VIII. 

Run-off. 

Ron-oCf — Influence of Various Factors — Relations of Annual Rainfall 
and Run-off of Water Year — Relation of Periodic Rainfall to Run- 
off — ^Monthly Keiatlon of Rainfall and Run-off — ^Maximum iStream 
Flow— Estimate of Stream Flow 146; 



Contents. zi 

CHAPTER IX. 

RuN-OFF» ( Continued ) 

Relation of Run-off to Topographical Conditions — Tweets of Geological 
Condition on the Run-off— The Influence of Storage on the Distri- 
bution of Run-off— Effects of Area on the Run-off — ^The Study of a 
Stream from Its Hydrographs — Comparative Run-off and Compara- 
tive Hydrographs — Comparative Hydrographs from Different 
Hydrologlcal Divisions of the United Statest— Literature 17S 



CHAPTER X. 

Stream Flow. 

Plow in Open Channels — Changes in Value of B^tors with Changes 
in Flow — Effects of Variable Flow on the Hydraulic Gradient — 
Effects of a* Rising or a Falling Stream on Gradient — Effects of 
Channel Condition on Gradient — Effect of Change in Grade and of 
Obstructions — Relation of Gauge Heights to Flow — Variations in 
Velocity in the Cross-Section of a Stream — Effects of Ice-Covering 
on the Distribution of Velocities 1»«. 



CHAPTER XI. 

The Measurement of Stream Flow. 

Necessity for Stream Flow Measurements — ^Methods for the Estimate 
or Determination of Flow in Open Channels--Estimates from 
Cross-Section and Slope — Weir Measurement — Measurement of 
Flow by the Determination of Velocity — The Use of the Current 
Meter — Current Meter Ob?ervatons and Com putatlon'— Float 
Measurements — The Application of Stream Gaugings — Literature. 21 Jl: 



CHAPTER XII. 

Water Whescls. 

Classification of Water Wheels — Gravity Wheels— Reaction Wheels — 
Impulse Wheels — ^Use of Water Wheels — Classification of Tvtr- 
bines— Conditions of Operation — Relative Advantage of Reaction 
and Impulse Turbines — Relative Turbine Efficiencies — Turbine De- 
velopment in the United States — The American Fourneyron Tur- 
bine—The American Jonval Turbine — The American Type of Re- 
action Turbine — The Double LefTel Turbine — Other American 
Wheels — ^Early Development of Impulse Wheels — American Im- 
pulse Wheels — Turbine Development In Europe 23 T 



:xxi 



Contenta, 



CHAPTER Xtll, 

Th§ Runner — Its Material and Manufacture — Diameter af tte Run* 
jier— The Detalli oC the Runiter — Vertical Turblae Bearlnga^— Hoii* 
fontal Turbine Bearings — Thrusts-Bearing In Snoqualmle Fall* 
Turblus— The Chute Case — Turbine Gates— The Draft Tube. 2S4 

tJHAPTER XIV. 

Htdbacxics of the TtniBirffi. 

"practical Hydraulics of the Turbine^NoniencIature Used la Chapter— 
First Principies^lmpuise and Keactlon— The impulse Wheel— 
irffect of Angle of Discharge on Efficiency^ — Reaction Wheel- 
Graphical Relation of Energy and Velocity In Reaction Turbine* 
Turbine Relations— Relation of Turbine Speed to Diameter and 
Head— Graphical Expression of Speed Relations— Relations of fp 
and Efficiency — Discharge of Turbine at Fixed Gats Openings 
Power of a Turbine — The Relation of Diacbarge to the Diameter of 
a Turbine — The Relation of Power to the Diameter of a Turbine — 
Relation of Bpeed to Di:?charge of Turbines.— Relations of Speed to 
Power or Turbines^ Value of Turbine Constants— Literature,,., 

CHAPTER XT. 

TunaiKE Testinq. 

The Importanrc of Testing Machinery — The Testing of Water Wheeli^— 
Smeatoa's Experiments — The Barly Testing of Turbine Water 
Wheels — The Testing of Turbines hy James Emerson— The Kolyoke 
Testing Flume — The Value of Tests — Purpose of Turbine Testings 
P^tors that Influence the Results of a Test — Measurement of Dl»> 
Charge — Measurement of Head — Measurement of Spetd of Rota- 
tion — Measurement of Power — Efficiency — Illustration of Methods 
and Apparatus for Testing Water Wheela— Tests of Wheels In 
Place— Literature ,,.* , ..^ ».., Sfl 



CHAPTER XVL 

The Seiactioh of the Tuhbie^i^ 

Eflert of Condttons of Operation — Baals for the Selection of the Tur- 
bines-Selection of the Turbine for Uniform Head and Power— Ths 
Selection of a Turbine for a Given Speed and Power to Work under 
a Given Fixed Head— To Estimate the Operating Results of a Tur- 
bine under one Head from Test Results Secured at Another Head — 
To Estimate the Operating Results of a Turbine of one Diameter 
from Test Results of Another Diameter of the Same Series— To 
Estimate the Operating Results of a Turbine under Variable 



Contents. xiii 

Heads from a Test Made under a Fixed Head — A More Exact 
Graphical Method fi)r Calculation^— The Construction of the Char* 
acteristlc Curves of a Turhlne — The Consideration of the Turbine 
from its Characterletlc Curve — Other Characteristic Curves — 
Graphical Analysis as Proposed by Mr. W A. Waters 884 

CHAPTER XVII. 

The Load Cubvb' and Load Factoes, and Theib Influence on thb Design or 

THE Power Plant. 

Variation In Load — Load Curves of Light and Power Plants.— Factory 
Load Curves — ^Load Curve of London Hydraulic Supply Company — 
Railway Load Curves — ^Load Conditions for Maximum Returns*— The 
Load Curve in Relation to Machine Selection — Influence of Manage- 
ment on Load Curve — Relation of Load Curve to Stream Flow and 
Auxiliary Power — Literature • 420 

CHAPTER XVIIL 

The Spied Regxtlation of Turbine Water Wheels. 

The Relation of Resistance and Speed — Self-Regulation in a Plant with 
Variable Speed and Resistance — ^The Relations Necessary for Con- 
stant Speed — ^The Ideal Governor — Present Status — Value of Uni- 
form Speed — ^The Problem — ^Energy Required to Change the Pen- 
stock Velocity — Hunting or Racing — ^Nomenclature — Shock of 
Water Hammer Due to Sudden Changes In Velocity — ^Permissible 
Rates of Gate Movement — ^Regulation of Impulse Wheels — Influences 
Opposing Speed Regulatiour- Change of Penstock Velocity — Effect 
of Slow Acceleration on Water Supplied to Wheel — Value of Racing 
or Gate Over-Run — Energy Required to Change the Penstock Velo- 
city—Effect of Sensitiveness and Rapidity of Governor — The Fly- 
wheel — ^The Stand-Pipe — ^The Air Chamber — Predetermination of 
Speed Regulation for Wheel set In open Penstocks — Predetermina- 
tion of Speed Regulation, Plant with Closed Penstock, — Predeter- 
mination of Speed Regulation, Plant with Standpipe — Application 
of Method. Closed Penstock — ^Application of Method, Open Penstock 
—Application of Method, Plant with Standpipe— Literature 440 

CHAPTER XIX. 

The Wateb Wheel Go\'ebnob. 

Types of Water Wheel Governors — Simple Mechanical Governors — ^Anti- 
racing Mechanical Governors — Details and Applications of Wood- 
ward Govemora— The Lombard-Replogle Mechanical Governors — 
Essential Features of an Hydraulic Governor— Details of Lombard 
Hydraulic Govemor^Operatlng Results with Lombard Governor — 
The Sturgess Hydraulic Governor — Test Results with Sturgess Gov- 



xiv . Contents. 

ernor — Control from Swltchboarfl — Connection of Governors to 
Gatea— Relief Valves — Lombard Hydraulic Relief Valves — Sturgess 
Relief Valves ...c 470 



CHAPTER XX. 

ABBAI7GEMENT OF THE REACTION WheEL. 

General Conditions — Necessary Submergence of Reaction Wheels^— Ar- 
rangement of Vertical Shaft Turbine — ^Arrangement of Horizontal 
Turbines— Classification of Wheels — ^Vertical Wheels and Their Con- 
nection — Some Installations of Vertical Water Wheels — Some In- 
stallations of Vertical Wheels In Series — Some Installations of 
Horizontal Water Wheels — Some Installations of Multiple Tandem 
Horizontal Wheels — ^Unbalanced Wheels 500 



CHAPTER XXI. 

The Selection of Machinery and Design of Plant. 

Plant Capacity — Influence of Choice of Machinery on Total Capacity- 
Effect of Size of Units on Cost — Overload — ^E#conomy In Operation- 
Possibilities in Prime Movers — Capacity of Prime Movers — The In- 
stallation of Tandem Water Wheels — Power Connection — ^Various 
Methods of Connection in Use— Use of Shafting— The Wheel Pit — 
Turbine Support— Trash Racks 525 



CHAPTER XXII. 
Examples of Watee Power Plants. 

Sterling Plant— Plant of York-Haven Water Power Company — Plant of 
South Bend Electric Company — Spier Falls Plant of the Hudson 
River Power Transmission Company — Plant of Columbus Power 
Company — Plant of the Dolgevllle Electric Light and Power Co. — 
Plant of the Shawlnigan Water and Power Company — Plant of the 
Concord Electric Company — Plant of Winnipeg Electric Railway 
Co. — Plant of Nevada Power, Mining, and Milling Co. — Literature. . 637 

CHAPTER XXIII. 

The Relation of Dam and Poweb Station. 

Ceneral Consideration — Classification of Types of Development — Con- 
centrated Fall — Examples of the Distribution of Water at Various 
Plants — Head Races only— Plants Located in Dam— High Head De- 
velopments • 661 



Contents. xv 

CaEIAPTER XXIV, 

PsmoiFLiB or CoNBTBucnoN or Dams. 

Object of Construction— Dams for Water Power Purposes^-Helght of 
Dam — ^Ayallable Head — 'Vhe Principles of Oonstmction of Damfr^ 
The Foundations of Dams — Strength of Dams — Flood Flowsr^Im? 
pervious Ctonstructionr-The Stability of Masonry Dam»— Calcula^ 
tions for Stability — Further Considerations— Types and Details of 
Dams— Literature 579 

CHAPTER XXV. 

Appendages to Dams. 

Movable Dams — Flood Gates — Flash Boards — Head Gates and Gate 

Hoists — Flshways — ^Logways — ^Literature 603 

CHAPTER XXVI. 

Pondage and Storage. 

Effect of Pondage on Power — ^Effect of Limited Pondage on the Power 
Curve — ^Power Hydrograph at Sterling, Illinois — Effect of Pondage 
on other Powers— Effect of Limited Storage — ^Effect of Large Stor- 
age — Effect of Auxiliary Power — ^EJffect of Maximum Storage — Cal- 
culation for Storage — ^Method of Storage Calculation — ^Analytical 
Method— Literature 624 

CHAPTER XXVII. 

Cost, Value and Sale of Poweik. 

¥*inancia] Consideration — Purpose of Development — Cost of Water Pow- 
er — Depreciation — ^Annual Cost of Developed Power— Cost of Distri- 
bution—Effect of Partial Loads on Cost of Power— Cost of Auxil- 
iary Power or Power Generated from other than Water Power 
Sources — Market Price of Water Pow^r — Sale of Power — ^An Equi- 
table Basis for the Sale of Power— Value of Improvements Intended 
to Bffect Economy— Value of a Water Power Property— Literature. 646 

CHAPTER XXVIII. 

The Investigation of Water Power Projects. 

The ESztent of the Investigationr— Preliminary Investigation and Re- 
port—Study of Kun-off- Study of Rainfall— Study of Topographi- 
cal and Geological Conditions — Study of Flood-flow — Study of 
Back Water Curve— Study of Head— Study of Storage and Pond- 
age — Study of Probable Load Curve — Study of Power Development 
Study of Auxiliary Power— Study of Site of Dam and Power Sta- 
tion — Study of Plant Designr— The Estimate of Cost — The Report. . 675 



I 



xvi Contents. 

APPENDICES. 

A. Water Hammer — B. Speed Regulation, a more Detailed Analysis 
than in Chapter XVIII— C. The Stand-Pipe — D. Test Data of Turbine 
Water Wheels— E. Elffect of an Umbrella upon Formation of Vor- 
tices— P, EJvaporatlon Tables— G. Two New Water Wheel Governors 
— H. Miscellaneous Tables Including: Equivalent Measures and 
Weights of Water— Equivalent Units of EJnergy— Velocities in Feet 
per Second Due to Heads from to 50 Feet— Three Halves Powers 
of Numbers, to 100 — Five Halves Powers of Numbers, to 50 — ^Re- 
lation of mean Rainfall to Maximum and Minimum Discharge 
of Various Rivers — Rainfall, Run-oft and Evaporation for Storage. 
Growing and Replenishing Periods or 12 Streams of the United 
States *.. 685-757 



WATER POWER ENGINEERING. 



CHAPTER L 



INTRODUCTION. 

THE HISTORY OF WATER POWER DEVELOPMENT. 

I. Early Development of Water Power. — Most methods of 
power generation can be traced to an origin at no very remote 
period. Their development has been within historic times. The 
first development of water power, however, antedates history. 
Its origin is lost in remote antiquity. 

Air and water, both physical agents most essential to life, have 
ever been the most obvious sources of potential energy and have 
each been utilized for power purposes since the earliest times. 
Beside the Nile, the Euphrates, and the Yellow Rivers, thou- 
sands of years ago the primitive hydraulic engineer planned and 
constructed his simple forms of current wheels and utilized the 
energy of the river current to raise its waters and irrigate the 
otherwise arid wastes into fertility. Such primitive wheels were 
also utilized for the grinding of corn and other simple power 
purposes. From these simple forms and primitive applications 
have gradually been developed the modern water power installa- 
tions of to-day. 

2. The Earliest Type of Water Wheel— The crude float wheel 
driven directly by the river current developed but a small por- 
tion of the energy of the passing stream. The Chinese Nora, 
built of bamboo with woven paddles, is still in use in the east 
(see Fig. i), and was probably the early form of development of 
^his type of wheel. The type is by no means obsolete for it is 
yet used for minor irrigation purposes in all countries. These 
^vheels, while inefficient, served their purpose and were exten- 
sively developed and widely utilized. One of the greatest de- 
velopments of which there is record was the float wheel installa- 



Introduction. 




Pig. 1, — Chinese Nora, or 



Float Wlieel Used 
Present. 



From Earliest Times to 



lion used to operate the pumps at London Bridge for the first 
water supply system of the city of London, and constructed 
about 1581 (see Fig. 2). In all such wheels the paddles dip into 
the unconfined current which, when impeded by the wheel, heads 
up and passes around the sides of the wheel and thus allows^ 
only a small part of the current energy to be utilized. H 

3. The Undershot Wheal, — The introduction of a channel con- 
fining the water and conducting it to a point where it could be 
applied directly to the undershot wheel, was an improvement that 
permitted the utilization of about thirty per cent, of the theo-J 







rig. E. — Float Wbeel Opemttng; Fiunps for Water Supply ot London 1S8 
(From Matthews' Hydraulia Loud. 1835.) 




The Overshot and Breast Water Wheel. 3 

retical power of the water. This form of water wheel was most 
widely used for power development until the latter half of the 
eighteenth century. 

In the float and undershot wheels the energy of water is ex- 
erted through the impact due to its velocity. The heading up 
of the water, caused by the interference of the wheel, results 
also iii the exertion of pressure due to the weight of the water, 
but this action has only a minor effect. The conditions of the 
application of the energy of water through its momentum is not 
favorable to the high efficiency of this type of wheels and the 
determination of this fact by Smeaton's experiments undoubt- 
edly was an important factor in the introduction and adoption of 
the overshot water wheel. 



.s^i^^i 



Fig. S.— Breast Wheel Used From About 1780 to About 1870. 

4. The Overshot and Breast Water Wheel. — In the overshot 
water wheel the energy of water is applied directly through its 
weight by the action of gravity, to which application the design 
of the wheel is readily adapted. Such wheels when well con- 
structed have given efficiencies practically equal to the best 
modem turbine, but on account of their large size and the serious 
effects of back-water and ice conditions, they are unsatisfactory 
for modern power plants (see Fig. 11). 

Following the work of Smeaton, the breast wheel (see Fig. 3) 
was developed in England largely through the work of Fairbairn 
^^^ Rennie. The latter in 1784 erected a large wheel of this 
^ype to which he applied the sliding gate from which the water 
flowed upon the wheel instead of issuing through a sluice as 
formerly. About this time the fly-ball governor, which had been 
^^igned and adapted as a governor for steam engines by Watt, 
^^ applied to the governing of these wheels and by means of 
these governors the speed of the wheel under varying loads was 



iDLroduclioo. 




Fig, 4.— Breast Wheel About 1790 Showing Early Application of Governor, 

(After Glynn.) 

kept sufficiently constant for the purpose to which they were 
then applied, (See Fig* 4*) 

Another mode of applying water to wheels under low falls was 
introduced by M. Poncelet, (See Fig< 5.) Various changes and 
improvements in the form of buckets, in their ventilation so as 
to permit of complete filling and prompt emptying, and in their 
structure, tcxjk place from time to time, and until far into the 
middle of the nineteenth century these forms of wheels were 
widely used for water power purposes. 




Fig. 5.— Poticelet's Wheel 



5. The Development of the Turbine. — The invention of any 
important machine or device is rarely the work of a single mind. 
In general such inventions are the result of years of experience 
of many men which may be simply correlated by some designer. 



Fundamental Idea of the Turbine. 



to 'whom often undue credit is g^ven* To the man who has 
gathered together past experiences and embodied them in a new 
and useful invention and perhaps through whose energy practical 
applications are made of such inventions, the credit is frequently 
assigned for ideas which have been lying dormant, perhaps 
through centuries of time. Every inventor or promotor of val- 
uable improvements in old methods and old construction is en- 
titled to due credttj but the fact should nevertheless be recalled 
that even in the greatest inventions very few radical changes are 
embodied, but old ideas are utilized and rearranged and a new 
and frequently much more satisfactory combination results. Im- 
provements in old ideas are the improvements which are the 
most substantial. Inventions which are radically new and strictly 
original are apt to be faulty and of little practical value* 



I 




^FH5. 6, — Anctent Indian Water WheeK (After Glynn J ContalnEng FuB^ 
dameutal Suggest ion of Both Turbine and Impulse Wlieela. 



6, Fundamental Ideas of the Turbine. — ^The embryo turbine 
may be distinguished in the ancient Indian water mill (see Fig. 6). 
A similar early type of vertical wheel used in Europe in the six- 
teenth century, the illustration of which was taken from an an- 
cient print (see Sci. Am. Sup* Feb. 17, '06) is shown in Fig- J. 
Barkers mill in its original form or in the form improved by 
M* Mathon de Cour, embodied the principal idea of the pressure 



6 Introduction* 

turbine, and was used to a considerable extent for mill purposes. 
In 1845 James Whitlaw suggested an improved form which was 
used in both England and Gennany early in the nineteenth cen- 
tury. (See Fig. 8.) Many elements of the modern turbine were 
conceived by Benjamin Tyler, who received letters patent for 
what he termed the "Wry Fly" wheel in 1804. T!ie description of 
this wheel as contained in the patent specifications is as follows : 




Fig. 7,— Early Vertical Wheel. 



Containing fundamental auggeatioii of tli» 
Turbine. 



'The Wr>' Fly is a wheel which, built upon the lower end of a 
perpendiciilar shaft in a circular form, resembles that of a tub. 
It is made fast by the insertion of two or more short cones, 
which, passing through the shaft, extend to the outer side of the 
wheel. The outside of the wheel is made of plank, jointed and 
fitted to each other, doweled at top and bottom, and hooped by 
three bands of iron, so as to make it water-tight ; the top must 
be about one-fifth part larger than the bottom in order to drive 



4 




Barker's MiU. 7 

the hoops, but this proportion may be varied, or even reversed, 
according to the situation of place, proportion of the wheel, and 
quantity of water. The buckets are made of winding timber, and 
placed inside of the wheel, made fast by strong wooden pins 
drove in an oblique direction ; they are fitted to the inside of the 
tttb or wheel, in such a manner as to form an acute angle from 
the wheel, the inner edge of the bucket inclining towards the 
w^ter, which is poured upon the top, or upper end of it about 
twelve and a half degrees ; instead of their standing perpendicular 
with the shaft of the wheel they are placed in the form of a 
screw, the lower ends inclining towards the water, and against 
the course of the stream, after the rate of forty-five degrees ; this, 
however, may be likewise varied, according to the circumstances 
of the place, quantity of water, and size of the wheel." 




Elevation. 




Plan and Partial Section. 

Fig. & — Early Vertical Wheel. Containinjir Fundamental Suggestion of the 
Tnrbine. (After Glynn. ) 



Inlroduction* 




Fig. 9. — ^Roue A* CurveB (After Glimii). 

From the description it will be noted that, with the exception 

of the chuteSp the principal features of the modern turbine were 
here anticipated. The "Wry Fly" wheel was an improvement on 
the "tub" wheel which was then in use to a considerable extend 
in the country. 

These various early efforts received their first practical con- 
summation and modern solution ihrough various French in- 
ventors early in the nineteenth century. The "Roue a Ciives*' 
(Fig. 9) and the **Roue Volant" {Fig. 10) had long been used 
in France, and were the subject of extensive tests by MM* Pio- 
bert and Tardy at Toulouse. Those various wheels received the 
water tangentially through an opening or spout, being practically 
an improvement on the old Indian mill by the addition of a rim 
and the modification of the form of buckets. 

7. The Modem Turbine, — The next improvement in the United 
States consisted in the addition of a spiral or scroll case to the 
wheel, by means of which the water was applied equally to all 
parts of the circumference passing inward and downward through 
the wheel. To the French inventors, Koechlin, Foumeyron and 
Jonval, is largely due the design of the turbine in a more modern 
and practical form. By the middle of the nineteenth century 
these wheels had met with wide application in France and been 



■ 

I 

4 



The Modern Turbine. 




I 



Fig. 10. — Roue Volant (After Glynn). 

adopted and considerably improved by American and German 
engineers, but were scarcely known in England. (See "Power 
of Water," by Jos. Glynn, 1852.) The turbine was introduced 
into the United States about 1843 ^Y Elwood Morris, of Penn- 
sylvania, but was developed and brought to public attention more 
largely through the inventions of Uriah A. Boyden, who in 1844 
designed a seventy-five horse-power turbine for use at Lowell, 
Mass, (See Fig. 132, page 251.) The great advantage of the 
turbine over the old style water wheel may be summarized as fol- 
lows: (See Figs. 11 and 12). 
First: Turbines occupy a much smaller space. 
Second: On account of their comparatively high speed they 
"CJin'frequently be used for power purposes without gearing and 
with a consequent saving in power. 
Third: They will work submerged. 

Fourth: They may be utilized under any head or fall of water. 
(Turbines are in use under heads as low as sixteen inches and 
as high as .several hundred feet.) 

Fifth: Their efficiency, when the wheel is properly constructed, 
« comparatively high. 

Sxth: They permit a greater variation in velocity without ma- 
terial change in efficiency. 



to 



Imroduclion. 




The Francis Turbine. 



zx 



Seventh: They are more readily protected from ice interfer- 
ence. 

8, The American or Francis Turbine. — ^Through the efforts of 
Uriah A. Boyden and James B. Francis (1849), ^^e Fouraeyron 
turbine became the leading wheel in New England for many 
years. 

In 1838 Samuel B. Howd of Geneva, New York, patented the 
"inward flow" wheel, in which the action of the Fourneyron tur- 
bine was reversed. This seems to have been the origin of the 
American type of turbine, and the Howd wheel was followed by 
a large number of variations of the same general design on 
which American practice has been based for many years. About 
^849, James B. Francis designed an inward flow turbine of the 
same general t3rpe as the Howd wheel. Two of these wheels 




IS. — Inward Flow Wheel by S. B. Howd t After Francis). 



^'cre constructed by the Lowell Machine Sliop for the Boott 
Cotton Mills. In the Lowell hydraulic experiments (page 61) 
^Jr. Francis refers to the previous patent of Howd and says : 
"Under this patent a large number of wheels have been con- 
structed and a great many of them are now running in diflferent 



I? 



Introduction. 



parts of the country. They are known in some places as the^ 
Howd wheels in others as the United States wheel. They have 
uniformly been constructed in a very simple and cheap manner 
in order to meet the demands of the numerous classes of millers 
and manufacturers who must have cheap wheels if they have 
any." M 

Fig. 13 shows a plan and vertical section of the Howd wheels 
as constructed by the owners of the patent rights for a portion 
of the New England states. In this cut g indicates the wooden 




Fig, 14, — Original Francis Turblna 

guides by which the water is directed on to the buckets; W ifi 
dicates the wheel which is composed of buckets of cast iroi! 
fastened to the upper and lower crowns of the wheel by bolts. 
The upright crown is connected with the vertical shaft S by arms. 
The regulating gate is placed outside of the guides and is made 
of wood. The upright shaft S runs on a step at the bottom (noi 
shown in the cut). The projections on one side of the buckets. 
it was claimed, increased the efficiency of the wheel by diminish^ 
ing the waste of the water. f 

The wheel designed by Francis was on more scientific lines, of 
lietter meclianical construction (see Fig. 14) and is regarded bi 




Modem Changes in Turbine Practice. 



13 



many as the origin of the American turbine. The credit of this 
design is freely awarded to Francis by German engineers, this 
type of wheel being known in Germany as the Francis Turbine. 
The Francis wheel was followed by other inward flow wheels of 
a more or less similar type. The Swain wheel was designed by 
A. M. Swain in 1855. The American turbine of Stout, Mills and 
Temple (1859), ^^^ Leffel wheel, designed by James Leflfel in 
i860, and the Hercules wheel, designed by John B. McCormick 
in 1876, are among the best known and earliest of the wheels of 
this class. 

9. Modem Changes in Turbine Practice. — A radical change has 
taken place in later years in the design of turbines by the adop- 
tion of deeper, wider and fewer buckets which has resulted in a 
great increase of power as shown by the following table from a 
paper by Samuel Webber (Transactions of Am. Soc. M. E. 
Vol. XVII) : 



T1811 h— Showing Size, Capacity and Power of Varimis Txirbinee Under 
a ee-foot Head. 



Inches 
Diameter. 



Cubic Feet 

Water per 

Second. 



Horse 
Power. 



Boyden-Fourneyron . . 

Ri«lon 

Bisdon "L. C." 

B»don"L. D." 

LeHel, Standard 

Wfel, Special 

Tyler.. 

SviiiL 

Hunt, "Swain bucket' 

Hnnt, New Style 

lAl, ••Samson" 

"Htttsoles" 

'TieU»'» 

^ 8wtin 



36 

:^6 

36 
36 
35 
36 
36 
36 
36 
35 
36 
25 
86 



22.95 
35.45 
48.27 
80. 
40.46 
60. 
40.7 
58.2 
48.8 
98. 
109.1 
107.6 
108.8 
89.5 



55 

89 
121 
199 

96 
148 

95.8 
140 
121 

289.74 
264 
253.5 
266 
215 



By 1870 the turbine had largely superseded the water wheel 
for manufacturing purposes at the principal water power plants 
in this country. The old time water wheel has since become of 
comparatively small importance, but it is still used in many iso- 
'^ places where it is constructed by local talent, and adapted 
to local conditions and necessities. 



14 Introduction. 

The current wheel is still widely used for irrigation purposes 
and in many instances is a useful and valuable machine. 

10. Historical Notes on Water Power Development. — ^Water 
mills were introduced at Rome about seventy years B. C. (see 
Strabo Lib. XII), and were first erected on the Tiber. Vitruvius 
describes their construction as similar in principle to the Egyp- 
tian Tympanum. To their circumference were fixed floats or 
paddles which when acted upon by the current of the stream 
drove the wheel around. Attached to this axis was another ver- 
tical wheel provided with cogs or teeth. A large horizontal wheel 
toothed to correspond with it worked on an axis, the upper head 
of which was attached to the mill stone. The use of such water 
wheels became very common in Italy and in other countries sub- 
ject to Roman rule. 

Some of the early applications of water power are of interest. 
In 1 581 a pump operated by a float wheel was established at 
London Bridge to supply the city of London with water. In 
1675 ^ri elaborate pumping plant driven by water wheels was 
established on the Seine river near Saint Germain. For this 
plant a dam was constructed across the river and chutes were 
arranged to conduct the water to the undershot water wheels. 
Thcse were twelve .pr more in number, each operating a pump 
that raised the waters of the Seine into certain reservoirs and 
aqueducts for distribution. 

The pumping of water for agricultural irrigation and drainage, 
domestic supplies and mine drainage, was undoubtedly the first 
application of water power, and still constitutes an important 
application of water. Fig. 15, from an article by W. F. Dupfec, 
published in Cassier's Magazine of March, 1899, illustrates a 
primitive application of the water wheel to the pumping of water 
from mines. The frontispiece also shows the great Laxy over- 
shot water wheel in the Isle of Man which is still used for mine 
drainage. The wheel is about seventy feet in diameter and the 
water is brought froin the hills a considerable distance for power 
purposes. 

11. Development of Water Power in the United States. — ^In 
this country one of the first applications of water power was the 
old tidal mill on Mill Creek near Boston, constructed in 1631, 
which was followed by the extensive developments of small 
powers wherever settlements were made and water power was 



Development of Water Power. 



IS 



available. Often availability of water power determined the 
location of the early settlement. 

About 1725 the first power plant was established along the 
Niagara River. This was a water-driven saw-mill constructed 



Ckronologieal Development of Water Power of the United States to 1898. 



Year. 



Lowell, Mass 

Nwhoa, N. H 

<5ohoee,N. Y 

Norwich, Conn 

ADgQBta,Me. , 

Mmchester.N. H , 

Hooksett, N. H 

Liwienoe, Mass. 

Aopirta,Ga 

Holyoke, Mass 

Uvnston, Me. 

Oolomboa, Ga 

Bocbeeter, N. Y 

St. Anthony Falls, Minn. . 
Kiagara,N. Y. (Hy. canal) 

Turner's Falls. Conn 

FoxRiver, Wis 

KiminghaiD, Conn 

Bingor, Me. 

Augusta, Ga 

timer's Falls. N. Y 

Mechanicsville, N. Y 

^ Cload, Minn 

little Falls. Minn 

Spokane, Wash 

Howland, Me 

^wtt Falls, Mont 

Aiatln, Texas. 

gwhSte. Marie, Ont 

Johom, Cal 

^id,N.H 

JWenajMont 

Junneapolis, Minn 

Mechanicsville, N. Y 



1822 
1823 
1826 
1828 
1834 
1835 
1841 
1845 
1847 
1848 
1849 
1850 
185(> 
1857 
18()1 
1866 
1866 
1870 
1876 
1876 
1882 
1882 
1885 
1887 
1888 
1888 
18<»0 
1891 
1S91 
1891 
1894 
1894 
1896 
1897 
1897 
:898 



Fall 
Ft. 



36 

36 
104 
16 
17 
52 
14 
30 
50 
50 
50 
25 
236 
50 
90 
35 
185 
22 
9 
50 
30 
20 
14 
14 
70 
22 
42 
60 
18 
55 
13 
170 
446 
32 
18 
18 



Minimum 
Horse 
Power. 



11,845 

1,200 

9,450 

700 

3,5U0 

12,000 

1,81'0 

11,000 

8,500 

14,000 

11,900 

10,000 

8,000 

15,500 

15,000 

10,000 



1,000 

1,767 

8,500 

1,125 

3,636 

4,500 

4,000 

18,000 

6,000 

16,000 

10,000 

10,000 

6,200 

5,000 

50,000 

2,U40 

10,000 

6,000 

3,270 



Drainage 

AreaSq. 

Miles. 



4,088 
516 
3,490 
1,240 
5,907 
2,839 
2,791 
4,625 
8,830 
8,000 
3,200 

14,900 
2,474 

19,736 
271,000 
6,000 
6,449 
2,000 
7,200 
6,830 
2,650 
4,476 

13,250 

11,084 
4,180 



22,000 
40,000 
51,600 



2,350 

271,000 

360 

14,900 

19,737 

4,478 



^7 the French to furnish lumber for Fort Niagara. Mr. J. T. 
Fanning gives the following list of the dates of establishing some 
^ the principal water powers of the United States : 

The last few years have witnessed a still more rapid develop- 
ment. The increase in manufacturing industries and other de- 



i6 



Inti'oduclJoo 



mands for power and energy, I lie increased cosi of coal, am 
improvement in electrical methods of generation and tram 
sion have all united to accelerate the development of water p 
plants. Water powers once valueless on account of their 
tance from centers of manufacturing and population are 
accessible and such powers are rapidly being developed and 
energy brought into the market. 




rig. 



IS.— Earl f Application of Undershot Water Wheel to Mtne 
Date Unknown (from C&ssiers Mag. March, 1S99J 



Dri 



LITERATURE. 



I 



AppletoTi*a Cy doped la of Applied Merhanlcs* Modem Me Chan la 

S, pp* 891-901. Description of the development of the 
Spon*s Dictionary of Knglneerlng. Barker's Mill, pp. 230-23&. 
do. Float Water Wheels (includtng undershot wheels), pp. 15 
do, Overshot Water Whet^ls, p, 2557. 

do. PoDcelet*s Water Wheels, p 2G(J0. ^H 

do. Turbine Water Wheels, pp. 3014-3023, ^| 

Knights Mechanical Dictionary, Vol. 3, Water Wheels, p. 27* 

bines, pp. 2C56-2C^8. 



i 



Literature. i7 

4. Emerson, James. Hydrodynamics. Published by author. Willimansett, 

Mass. 1892. Describes several types of American turbines. 

5. Matthews, William. Hydraulia. London, 1836. (Description of London 

Bridge Water Wheels, p. 28.) 

6. Palrbairn. William. Machinery and Mill work. Description of undershot 

water wheel, pp. 145-150; description of earlier types (^ tur- 
bines, pp. 151-173. 

7. Francis, James B. Lowell Hydraulic Experiments, pp. 1-70. Descrip- 

tion and tests of Boyden-Fpurneyron Tremond Turbines; also 

the Boyden-Francls "Center-Vent" Turbine, in which the Flow 

was Radially Inward. New York, D. Van Nostrand, 1883. 
& Welsbach, P. J. Mechanics of Engineering, vol. XL Hydraulics and 

Hydraulic Motors. Translated by A. J. DuBois. New York. 

J. Wiley & Sons. 
9. Morin, Arthur. Experiments on Water Wheels having a Vertical Axis, 

Called Turbines, 1838. Translated by EUwood Morris in Jour. 

Franklin Inst, 3d ser.. vol. 6, 1843. pp. 234-246, 289-302. 370-377. 

370-377. 

10. Morris, ESlwood. Remarks on Reaction Water Wheels Used in the 

United States and on the Turbine of M. Foumeyron. Jour. 
Franklin Inst, 3d ser.. Vol. 4, 1842, pp. 219-227, 289-304. 

11. Morris, EUwood. Experiments on the Useful Effect of Turbines in the 

United States. Jour. Franklin Inst., 3d ser.. Vol. 6, 1843, 
pp. 377-384. 

12. Wbitelaw, James. Observations of Mr. EUwood Morris's Remarks on 

Water Wheels. Jour. Franklin Inst, 3d ser.. Vol. 8, 1844. 
pp. 73-80. 

13. Franklin Institute. The Koechlin Turbine. Jour. Franklin Inst, 3d 

ser.. Vol. 20, 1850, pp. 189-191. (Report of experiments made 
by members of the institute at the request of Emile Qeyelin, 
who introduced the Koechlin turbine at Dupont's powder mill.) 

H. Ewbank, Thos. Hydraulic and Other Machines for Raising Water. New 
York, 1847. 

15. Qeyelin, Emile. Experiments on Two Hydraulic Motors, Showing the 
Comparative Power Between an Overshot Wheel and a Jonval 
Turbine made for Troy, N. Y. Jour. Franklin Inst. 3d ser.. 
Vol. 22, 1851, pp. 418, 419. 

16 Glynn, Joseph. Power of Water. London, 1850. pp. 39-97. Weales 
Scientific Series. 

17. Webber, Samuel. Ancient and Modem Water Wheels. Eng. Mag., Vol. 1, 

1891, pp. 324-331. 

18. Frlzell, J. P. The Old-Time Water Wheela of America. Trans. Am. Soc 

C. E., Vol. 28, 1893, pp. 237-249. 

^5- Aldrlch, H. L. Water Wheels. Description of Various Types of Ameri- 
can Wheels. Power, Vol. 19, No. 11, 1894. 

20. Francis, James. Water Power in New England. Eng. Rec, Vol. SS» 
1896. pp. 418, 419. 
1 



1 8 Introduction. 

21. Geyelin, Emile. First Pair of Horizontal Turbines ever Built Working 

on a Ck>nimon Axis. Proc. Eng. Club, Philadelphia, Vol. 12, 

1895. pp. 213, 214. 

22. Francis, James. Water Power in New England. Eng. Rec. Vol. 33, 

1896, pp. 418, 419. 

23. Webber, Samuel. Water Power, its Generation and Transmission. Trans. 

Am. Soc. Mech. Eng., Vol. 17, 1896, pp. 41-57. 

24. Tyler, W. W. The BJvolution of the American Type of Water WhoeL 

Jour. West Soc. Eng., Chicago, Vol. 3, 1898, pp. 879-901. 

25. Johnson, W. C. Power Development at Niagara. Jour. Asso. Eng. Soc, 

July, 1899, pp. 78-90. Hist of early development of power at 
Niagara. 

26. Christie W. W Some Old-Time Water Wheels. Description of Various 

old wheels in Eastern U. S. Eng. News, Vol. 42, 1899, pp. 
394-395. 

27. Ruchel, E. Turbines at the World's Fair, Paris, 1900. Review of Tur- 

bine development in various countries. Zeitschr. d ver Deutsch, 
Ing. p. 657. 1900. 

28. Foster, H. A. The Water Power at Holyoke. Jour. Asso. Eng. Soc., Vol. 

25, 1900, pp. 67-34. 

29. Thomas. R. Development of Turbine Construction. Zeitschr. d ver 

Deutsch. Ing. p. 409, 1901. 

30. Rice, A. C. Notes on the History of Turbine Development in America. 

Eng. News, Vol. 48, 1902, pp. 208-209. 

31. Fanning, J. T. History of the Development of American Water Powers. 

Rept 22d Ann. Meeting, Am. Paper and Pulp Asso., 1898, pp. 
16-24. Progress in Hydraulic Power Development Eng. Rec- 
ord, Vol. 47, 1903, pp. 24-25. 

32. Fanning, J. T. Progress in Hydraulic Power Development BJng. Rec- 

ord, Jan. 3d, 1903. 

33. Slckman, A. F. The Water Power at Holyoke. Jour. N. E. W. W. Afi80.» 

Vol. 18, 1904, pp. 337-351. Historical. 



CHAPTER II. 

POWER. 

12. The Development of Potential Energy. — ^The development 
of natural sources of potential energy, the transformation of such 
energy into forms which can be utilized for power, and its trans- 
mission to points where it can be utilized for commercial pur- 
poses, constitutes a large portion of the work of the engineer. 
The water power engineer primarily deals with energy in the 
form of flowing or falling water, but his knowledge must extend 
much further for he encounters other forms of energy at every 
turn. Much of the energy available from the potential source 
will be lost by friction in bringing the water to and taking it 
from the wheel. Much is lost in hydraulic and mechanical fric- 
tion in the wheel ; additional losses are sustained in every trans- 
formation, and, if electric or other forms of transmission are 
used or auxiliary power is necessary for maintaining continuous 
operation, the engineer will be brought in contact with energy 
in many other forms. 

13. Definition of Energy. — Energy is the active principle of 
nature. It is the basis of all life, all action, and all physical 
phenomena. It is the ability to exert force, to overcome resist- 
ance, to do work. All physical and chemical phenomena are but 
"manifestations of energy transformations, and all nature would 
DC rendered inactive and inanimate without these changes. 

14. Solar Energy the Ultimate Source. — A brief consideration 
<^f the various sources of potential energy makes the fact mani- 
fest that solar energy is the ultimate source from which all other 
forms are directly or indirectly derived. The variations in solar 
heat on the earth's surface produces atmospheric currents often 
^f tremendous power. This form of energy may be utilized, in 
*ts more moderate form, to drive the sailing vessel and the wind- 
n^JI, and in other ways to be of service to man. The energy of 
fuel is directly traceable to solar action. Through present and 
past ages it has been the active cause of chemical and organic 



20 Power 

change and growth. From this has resulted fuel supplies avail- 
able in the original form of wood, or in the altered forms, from 
ancient vegetation to the forms of coal, oil and gas, and from 
which a large portion of the energy utilized commercially is 
derived. 

A brief study of meteorological conditions shows that through 
the agency of solar heat, and the resulting atmospheric move- 
ment, a constant circulation of water is produced on and near 
the earth's surface. Hundreds of tons of water are daily evapor- 
ated from the seas, lakes, rivers and moist land surface, rise as 
vapor into the atmosphere, circulate with the winds, and, under 
favorable conditions, are dropped again upon the earth's surface 
in the rainfall. Those portions of the rain that fall upon the 
land tend to flow toward the lower places in the earth's crust, 
where lie the seas and oceans, and such portions of these waters 
as are not absorbed by the strata, evaporated from the surface 
or utilized in plant gfrowth, ultimately find their way to theSe 
bodies of water to again pass through this cycle of changes which 
is constantly in progress. Thus we find water always in motion, 
and always an active agent in nature's processes. Due to its 
peculiar physical properties and chemical relations, it is one of 
the essential requisites of life, and is also of great importance in 
nature's processes through the energy of which it is the vehicle. 

15. No Waste of Energy in Nature. — Active continuous en- 
ergy transformation is^a most important natural phenomenon. 
Changes from one form to another are constantly in progress. 
In nature's transformations energy is always fully utilized. As 
the running stream plunges over the fall, the potential energy, 
due to its superior elevation, is transformed into the kinetic en- 
ergy of matter in motion, and through the shock or impact the 
kinetic energy is transformed into thermal energy due to a higher 
temperature, which again may be partially changed in form by 
radiation or vaporization. Thus the quantity of energy is con- 
tinually maintained, while its quality or conditions constantly 
vary. There is, and can be, no waste or loss of energy as far as 
nature itself is concerned. Wasted or lost energy are terms that 
apply only to energy as utilized in the service of man. Nature 
itself never seems to utilize the entire quantity of energy from 
one source for the development of energy of a single form, but 
always differentiates from one form into a number of other forms. 
When the engineer therefore attempts to utilize any source of 



Laws of Energy Conservation. 2i 

potential energy for a single purpose, he at once encounters this 
natural law of differentiation and finds it impossible to utilize 
more than a portion of the energy used in the manner in which 
he desires to utilize it. Much of this loss may be due to the form 
of energy available, much to the medium of transformation and 
transmission, and much to physical difficulties which it is im- 
possible to overcome. 

i6. Laws of Energy Conservation. — Primarily it should be 
fully understood and clearly appreciated that matter and energy 
can neither be created nor destroyed. Both may be changed in 
form or they may be dissipated or lost so far as their utilization 
for commercial needs is concerned. But in one form or another 
they exist, and their total amount in universal existence is al- 
ways the same. In any development for the utilization, trans- 
formation or transmission of energy, the following fundamental 
axioms must be thoroughly understood and appreciated: 

First : That the amount of energy which can be actually utilized 
in any machine or system can never be greater than the amount 
available from the potential source. 

Second: That the amount of energy which can be utilized in 
any such system can never be greater than the difference be- 
tween the amount entering the system and the amount passing 
from the system as waste in the working medium. 

17. Efficiency. — Efficiency is the ratio or percentage of energy 
utilized to energy applied in any system, part of a system, ma- 
chine or in any combination of machines. 

The efficiency df a given machine or mechanism, or the per- 
centage of available energy which can be obtained from a given 
system of generation and transmission therefore can never be 
greater than represented by the equation : 

E E' 

Efficiency or amount of available energy = — =; — in which 

E equals the energy in the working medium entering the machine 

E' equals the energy in the working medium passing from the machine. 

18. Natural limit to efficiency. — The total energy in a workins; 
medium such as water, steam, air, etc., is the energy measured 
from the basis of the absolute zero for the medium which is 
being considered. For example, the average surface of I_^ke 
Michigan is 580 feet above sea level ; each pound of water, there- 
fore, at lake level contains 580 foot pounds of potential energy. 
This amount of energy must therefore be expended in some man- 



22 Power. 

ner by each pound of water passing from the lake level to the 
ocean level, which may be regarded as the absolute zero refer- 
ence plane for water power. This energy cannot be utilized at 
Chicago for there no fall is available. A small portion of this 
energy is now utilized in the power plants at the falls of Niagara. 
Some energy will be ultimately utilized on the Chicago Drainage 
Canal, where a fall of some thirty-four feet is available from the 
controlling works to Joliet. Perhaps ultimately in its entire 
course one hundred and seventy feet of fall may be utilized by 
the waters of the drainage canal, in which case the absolute avail- 
able energy of each pound of water cannot be greater than shown 
by the following equation : 

Available energy = ^ — = ^^ = .2931, or 29.31 per cent. 

With any other form of energy the same conditions also pre- 
vail. Consider a pound of air at 760 degrees absolute tempera- 
ture Fahr., and at 75 pounds absolute pressure. The number of 
heat units contained will be given by the equation : 

Heat units = temperature X weight X specific heat. 

B. T. U. = 760 degrees XIX .1«^> = 128. 

To Utilize all of the energy in this air, it would be necessary 
to expand it down to a temperature of absolute zero and exhaust 
it against zero pressure. In any machine for utilizing com- 
pressed air, it will be necessary to exhaust it against atmospheric 
pressure. This will expand the air 3.10 times, and if expanded 
adiabatically it will have a final temperature of 474 degrees. The 
heat units in the exhaust will therefore be as follows : 

B. T. U. = 474 degrees X 1 X .169 = 80, 

and the available energy will be as follows : 

228 80 48 

Available energy = — = -^ = .375, or 37.5 percent. 

In this case also the temperatures vary directly as the heat 
units, and are therefore a measure of available energy: 

A -1 ui 760 — 474 rt-»r o- m 

Available energy = ^r-r-r — = .375 or 3/. 5 per cent. 

/oU 

In the ideally perfect furnace the efficiency is somewhat higher. 
The fuel may be consumed at a temperature of about 4,000 Fahr. 
absolute, and the gas may be cooled before escaping to about 600 
Fahr. In this case the possible efficiency or available energy is: 



Practical Limits to Efficiency, 23 

4000 660 

Available energy = -^^ — = .832 or 83.2 per cent. 

The above examples show, therefore, the limits which nature 
itself places on the proportion of energy which it is theoretically 
possible to utilize. For such losses the engineer is not account- 
able except for the selection of the best methods for utilizing 
such energy. The problem for his solution is, what amount of 
this available energy can be utilized by efficient machines and 
scientific methods. 

19, Practical Limits to Efficiency. — The preceding equations 
are the equations of ideally perfect machines. Of this available 
energy only a portion can be made actually available. In practice 
we are met with losses at every turn. Some energy will be lost 
in friction, as radiated heat, some in the slip by pistons, or as 
leakage from defective joints. In many other ways the energy 
applied may be dissipated and lost. From this it follows : 

The amount of energy which can be utilized can never be 
greater than the difference between the amount supplied to any 
given machine or mechanism, and the amount lost or consumed 
in such machines by friction, radiation or in other ways. Hence 
it follows that the efficiency of a given machine, or the percent- 
age of energy available, or which can be obtained from the ma- 
chine, can never be greater than the following: 

!,« . E — fE' +E' + E"-fE"etc.). , . . 
Efficiency = ^ • ^ ' in which 

B 8 total energy available 

E* E' E" etc. = the energy lost in friction and in various other ways, in 
the machine or system, and rejected in the exhaust from the same. 

Every transmission or transformation of energy entails a loss, 
hence, starting with a given quantity of energy, it gradually dis- 
appears by the various losses involved in the mechanism or ma- 
chines used. Other things being equal, the simpler the trans- 
niission or transformation, the greater the quantity of the orig- 
inal amount of energy that can be utilized. 

The term efficiency as here applied represents always the ratio 
"Ctween the energy obtainable from the mechanism or machine 
and the actual energy applied to it. 

Therefore the efficiency of a pumping engine is the ratio be- 
tween the energy of the water leaving the pump and the energy 
^ the steam applied to the engine. 



24 



Power. 



The efficiency of a hydro-electric plant is the ratio between the 
energy in the electric current delivered at the switch board and 
the energy in the water entering the water wheel. 

The efficiency of the dynamo in the same plant is the ratio be- 
tween the energy furnished by the dynamo and the energy ap- 
plied to it. 

If a shaft receives from an engine lOO horse power and de- 
livers 90, ten horse power being lost in friction, etc., the efficiency 
of the shaft transmission is 90 per cent. 

If a steam engine receives 1,000,000 heat units from the steam 
it uses, and is able to deliver only the equivalent of 10,000 heat 
units; i. e., 7,780,000 foot pounds of work, the efficiency of the 
engine is only one per cent. 

20. Efficiency of a Combined Plant. — In any plant or connected 
arrangement of mechanisms and machines for the transforma- 
tion or transmission of energy the efficiency of the plant is the 
product of the efficiency of each of its parts. 

Hence, to estimate total efficiencies, the efficiency of each part 
may be estimated, and the combined efficiency then obtained. 
From the same calculation, the necessary relations between the 
input and the output of energy can be obtained. Thus, if a 
boiler has an efficiency of 50 per cent., and an engine has an 
efficiency of 10 per cent., the combined efficiency will be .50X.10 
=.05 or five per cent. 

In the following examples the loss and efficiency of the unit 
and the combined efficiency of the various units in the system 
are shown. 

FIRST EXAMPLE. 
Example of Energy Loss in Well-Designed Steam Power Plant. 



Per Cent 

Lost. 



Per Cent 
Efficiency 



Furnace 

Ik)iler 

Steam Pipe 

Enjijine 

Belt 



Shafting, Belts and Counter Shafts 

Lathes or other Machine Tools 

Percentage of original energy utilized 
useful work 



20 
15 

5 
94 

5 

40 
60 



80 

85 

95 



95 
(K) 
50 



Net Effi- 
ciency from 
Potential 
Source. 



80 

68 

64.5 
3.87 
3.67 
2.2 
1.1 

1 1 



Efficiency of a Combined Plant. 



25 



SECOND EXAMPLE. 
Exampie of Energy Lo9B in Ilydfnulie Plant for Electric Lighting, 





Per Cent 
Lost. 


Percent 
Efficiency 


Net Effi- 
ciency from 
Potential 
Source. 


H4^ And Tnil Raree . . 


5 

20 

15 

6 

5 

8 

10 

20 

80 


95 
80 
85 
95 
95 
92 
90 
80 
20 


95 


Turbine. 


76 


Gearing 


64 6 


Shaft .'.; 


60 37 


Belt 


57 35 


Generator 


52.76 


Line Loss 


47 48 


Tranftformer .• 


87.98 


JjAinp ...c ..*.x 


7 00 


Percentage of original energy utilized in 
oaef ul work .* 


7.60 











THIRD EXAMPLE. 
Example of Energy Lost in Steam and Electric Pumping Plant 



Per Cent 
Loet. 



Per Cent 
Efficiency 



Net Effi- 
ciency from 
Potential 
Source. 



Boiler and Furnaco. 

bteam Pipe 

Eneine 

Belt 



Generator. 

Line 

Motor 

Pomp. 



Suction and Discharge Pipe 

PercentRge of original energy utilized in 
oseful work 



30 
5 

90 
5 
20 
10 
10 
26 
20 



70 
95 
10 
95 
80 
90 
90 
75 
80 



70 

66.6 
6.65 
6.82 
5.05 
4.55 
4.09 
3.06 
2.45 

2.45 



21. Capacity of Each Part of a System Not IdenticaL — In each 
of the transmission systems outlined above a much larger 
amount of energy enters the first unit of the system than is de- 
livered by the last. Each unit in the system receives a decreas- 
ing amount of energy. 

In consequence, the first units in the system must be of greater 
proportional capacity, and in practice each unit must be selected 
of a size or capacity suited for its position in the system. Thus 
in the first example, for each 100 units of energy rereived by the 
furnace, the engine receives but 64.5, and the shafting but 4. 



26 Power, 

aa. The Analysis of Losses. — In estimating power losses the 
loss in each step from the generation to the utilization of the 
power should be carefully examined. Four steps may ordinarily 
be considered in any system : 

1. Generation of power from potential source. 

2. Conversion of power into form for transmission. 

3. Transmission of power. 

4. Utilization of power. 

An analysis of the first three items is shown in Table 11. In 
Table III is shown the ordinary maximum and minimum ef- 
ficiencies obtained from various motors and machines in prac- 
tical work. Higher efficiencies are sometimes obtained under 
test conditions where great attention is g^ven to secure favorable 
conditions, and, in many places where careless work is permitted, 
neglect and unsatisfactory conditions will result in much lower 
efficiencies than the minimum shown. 

as. The Losses in a Hydro-electric Plant — ^To emphasize and 
point out in greater detail the various losses encountered in the 
generation and transmission of energy, especially as applied to 
hydro-electric plants, attention is called to Fig. 16. In this 
diagram is traced the losses from the potential energy of the 
water in the head race of the power plant to the power avail- 
able at the point where it is used. In each case considered it is 
assumed that 1,000 horse-power of energy is applied to the par- 
ticular work considered. 

First, consider the transmission of power for traction pur- 
poses. If a certain head is available when no water is flowing 
in the raceways, that head becomes reduced at once when the 
wheels begin to operate. A certain amount of head is also lost 
in order to overcome the friction of flow through raceways, racks 
and gateways. In the problem here considered it is assumed 
that the above losses are five per cent, of the total energy avail- 
able in the head-race, and that this loss occurs before the water 
reaches the turbines : hence, 95 per cent, of the potential energy 
is available at the turbine. The turbine loss is here assumed to 
be about 20 per cent. First-class turbines under three-quarter 
to full load conditions, will commonly give 80 per cent, efficiency, 
or a little better. 

Professor Unwin, in his "Development and Transmission of 
Power," page 104, gives the following percentage of loss in tur- 
bines : 



The Losses in a Hydro-Electric Plant. 



27 



Shafting, friction and leakage 3 to 5 per cent 

Unutilized energy 8 to 7 per cent 

Friction in shaft, guides and passages 10 to 15 per cent. 

Total loss of energy IG to 27 per cent 

TABLE II. 



Method of Generation. 



z 



J* 


z 



•-i 

X 

< 
H 

z 

<^ 

z 



< 

z 



Fuel. 



'Internal Coinhustion Engine 

Gas — Oil Engine losses. 

( Direct (Vacuum Pump) C Furnace. 
Steam ] i Boiler. 

( Indirect I Piping. 

(Direct (Ram) Ram losses. 
Indirect (Wheels) ) ^WoL^.'-' 



h 

a H 

2 






''I 



a 



o 

I 

i 

i 

< 

h 
O 

c 
o 

' i 



Water 
Power. 



Minor 
Sources. 



Electric (Primary Batteries) . 

Wind (Mills) 

Waves (Motors) 

^Sun Heat (Solar Engines) . . . 



" Various mechani- 
cal and other 
losses due to 
method used. 



" Internal Combustion Engine Included in engine 



Steam. 



Electrical . 



Engine and con- 
nection losses. 

Dynamos and wire 
losses. 



Hydraulic Pump 1 

Pneumatic Compressor losses. 

f Direct connected,— Shaft f 

Mechan- i Cables, Ropes, Ch:iins ) Various losses due 

ical I Electric ] to method need. 

tCombination (, 

(Entrance head. 
Pipe friction. 
Mmor losses. 
Connections. 



Electrical . 



Pnenmatic . 



fTran former losses. 
j Wire losses. 
I Motor losses. 
[Connections. 

(Pipe friction. 
Air cooling. 
Motor lossep. 
Connections. 



The Losses in a Hydro-electric Plant. 29 

The next loss shown on the diagram is the loss in transmitting 
the energy through the bevel gear and the shafting to the gen- 
erator. The loss in gearing, shafting, etc, is shown as 10 per 
cent., which is probably much less than actually takes place in 
most plants of this kind, but may be considered as representing 
the results of good practice. 

The loss in the transformation of power in the generator is 
given as 8 per cent. The generator is an alternator, and the cur- 
rent generated would be at about 2,300 volts. This current must 
be raised to a higher voltage, by means of transformers, for 
long distance transmission. These transformers would g^ve an 
efficiency of about 96 per cent. The line loss is dependent on the 
size of the copper used, but would probably not exceed 10 per 
cent. At the distributing point, where the energy is to be used, 
the high voltage current must be transformed again into suit- 
able voltage for distribution. The same energy loss is estimated, 
for these transformers. If the current is to be used for traction 
purposes, it will be necessary to convert it into direct current 
by means of a rotary converter, the efficiency of which is esti- 
mated at 92 per cent. The voltage from the general distribution 
system would probably be too high for direct use in the rotary 
converter, and would have to be transformed to a lower voltage 
before passing into the converter. A loss of about 6 per cent., 
therefore, should be allowed for this transformation. 

The current from the rotary converter is subject to a line loss 
which may be again assumed at 10 per cent. The loss in the car 
vQxAor may be estimated at 7 per cent. The percentage of loss 
and the percentage of efficiency for each unit in this generation 
and transmission system is based, of course, on the actual energy 
supplied by the unit next previous to it in the system, so that 
the percentages mentioned are not based on the total potential 
power available in the head-race but on the power actually reach- 
ing the machine. 

In the solution of any actual problems of this character it is 
necessary to determine the efficiencies of the various units of 
4c plant under the condition of actual service. The efficiency 
will be found to vary under various conditions of load. It may 
therefore be desirable to determine the probable losses under 
various working conditions. 

In the selection of the various machines which are to form a 
part of such a system of transmission, the choice should be 



30 



Power, 



based on an effort to establish a plant which will give the maxi- 
mum economy when all conditions of loading are considered. 
The losses in the transmission of power for traction purposes, 
as shown on the diagram, may be traced through in tabular 
form as follows: 



Total Energy 
Available. 



Per Cent 
Lose. 



Per Cent 
Efficiency 



1,000 HOBSK 

Power. 



LoBsin 
horsepower 



Head race 

Turbine 

Shaft and gearing 

Generator 

TransformerB. 

Transmission line. 

.Step-down Transformers. 
Secondary Transformers. 

Rotary Converters 

Line 

Traction Motor 



5 

20 

10 
« 
4 

10 
4 
6 
8 

10 
7 



95 
80 
90 
92 
96 
90 
96 
94 
92 
90 
93 



50 

UK) 

76 

64.7 
25.2 
60.4 
21.7 
31.3 
39.3 
45.1 
28.4 



Power utilized for operating the cars, or 37J per cent of the 
original energy 374 .5 Horse Power. 

In the generation and transmission of power for lighting pur- 
poses, the losses will be similar to those above mentioned, up 
to and including the step-down transformers at the point of dis- 
tribution. In this case, however, no secondary transformers or 
rotary converters would be necessary. The only loss between 
the step-down transformers and the light will be the line loss 
assumed at 5 per cent. The loss in the individual transformer 
for the light will be about 8 per cent., leaving the available en- 
ergy for actual use in the lamp at about 456.2 horse power, or a 
little less than 46 per cent, of the total energy in the head-race. 

In the case of the utilization of this energy for manufacturing 
purposes, the loss would be the same up to and including the 
step-down transformers at the point of distribution. The line 
loss in the distribution from the transformer house to the manu- 
facturing establishment may be assumed at 5 per cent. The 
motor, if properly selected, may be run at the line voltage, and 
no transformer losses need be considered. The motor efficiency 
is here shown at 92 per cent., although in most cases the per- 
centage of efficiency would be considerably less. 

The belt loss in transmitting the power from the motor to the 
line shafting is estimated at 5 per cent. 



Efficiency of Generators and Motors. 
Tablb m. — Ordinarif Ejfloiency of Oenerators and Motors, 



31 



Glass or Maceinsbt. 



Cent at Fcll 
Load, 



mum. 



Mini- 
mum« 



Water Wbeds. 



CoDdesaiii^ - - * - { 
gleam Engines . { **"" 

Kon-CondeneSng ) 
Steam Engines.. }**"" 

BefttEngmei. i> *#«« 

Gteom Air Compreadon . 

^llotor 

Bectrical Macbintry . , . 

Tnmamitting Mechaix- 



TmuDusaioD Methods. 



f Overaliot WJieels. ♦ - 

Bn^flSi Wheels' . 

Undershot Wheels . 

Tarbhiw 

Impulse Wheela. > . . 



i Boilers ^ - « . < 
\ Steam Pipe 



f Triple Expansion Corlij^ 
Compfitind GorUBS 
.Simple CorliBa 
Compound High Speed * . 



f Cbtnponnd Corllea 

1 Simple CorlisB 
Compound tliurh Speed, 
Simple Uif^h^peed. . ., , 
Simple Slide Val?e . . . . . 



iGas or Oil Engines . 
Diesel Motor 



'Compound Con. Corliss* 

Simple Con. Corliss . 

Simple Corliss*,***. ***, 
High Pressure 

^SmallStraijfht Line. .... 



5 Air^ cold 

( Air J reheated. 



r Dynamos .... 
! Motor, large.. 
\ MotoFi email , 
[Trans I or user.. 



fBelt .•.,.. 

Hope . * 

Cable. .- ...,, 

Direct connection 

Shafting ** 

Gearing - 

Bevel Gefiring 



Pneumatic r per mile , 
Hydraulici |^r mile * 
ElectriCr usual 



75 

iS5 
40 
S5 
85 

75 

18 
15 
12 
12 

12 

7 
7 

20 
30 

12 
2 

3 

60 
7U 

92 
90 
85 

95 

^7 
tm 
ln> 

S5 
75 

97 

ys 

»5 



65 
60 

25 
60 
75 

60 

75 

15 
12 

10 
10 

10 

7 
7 
6 
5 

10 
25 

10 
7 
5 
3 
IS 

SO 
60 

SO 
80 
75 
50 

85 
90 

75 
95 
70 
50 
60 

9^ 
90 
85 



32 Power. 

The shafting necessary for the general distribution of power 
through the factory is estimated at 75 per cent, efficiency. 

The belt loss from the shaft to the individual machine is esti- 
mated at an additional 5 per cent., leaving the total energy avail- 
able for use in the machine at 308.8 horse power, or about 31 per 
cent, of the original energy in the head-race. 

It should be noted that in each of the three transmission sys- 
tems mentioned above, the actual power utilized at the point of 
application is less than half of the energy available in the head- 
race. It is the function of the engineer to see that these losses 
are reduced to the greatest practicable extent. These losses 
must be limited in both directions. They must not be too great, 
nor too small. Tliey must be adjusted at the point where true 
economy would dictate. This limit is the point where the cap- 
italized value of the annual power lost is equal to the capitalized 
cost of effecting further saving. In other words, true economy 
means the construction of a plant that will save all the power 
or energy which it is financially desirable to save, and will per- 
mit such waste of energy as true economy directs. 

24. Units of Energy. — Energy is known by many names and 
exists in many forms which seem more or less independent. The 
principal forms of energy are measured by various units. Those 
most commonly considered in power development and trans- 
mission are as follows: 

Work is energy applied to particular purposes. In general it 
is energy overcoming resistance, mechanically it is .the exertion 
of force through space. 

Power is the rate of work, or the relative amount of work done 
in a given space of time. 

The unit of work is the foot pound, or the amount of work 
required to raise one pound one foot. One pound raised one 
foot, one-tenth pound raised ten feet, ten pounds raised one- 
tenth of a foot, or any other sub-division of pounds and feet 
whose product will equal one requires one foot-pound of work 
to perform it. 

The unit of power is based on the unit of work, and is called 
"horse power.'* It is work performed at the rate of 550 foot 
pounds per second, or 33,000 foot pounds per minute. 

Units of Heat. The unit of heat is the amount of heat which 
will raise one pound of water from 39 degrees Fahr. to 40 degrees 
Fahr. at atmospheric pressure. It is called the British Thermal 
Unit, and is indicated by the initials B. T. U. 



Conversion of Energy Units. 33 

Electric Unit. The unit of quantity of electricity is the coulomb. 
One coulomb per second is called an ampere, and one ampere un- 
der a volt pressure is equal to a watt, the unit of electric power. 

Water Power. Water power is the power obtained from a 
weight of water moving through a certain space. In water power 
the unit of quantity may be the gallon or the cubic foot ; the unit of 
head may be the foot; and the unit of time may be the second or 
minute. The weight of water, unless highly mineralized, at ordi- 
nary temperature, varies from 62.3 to 62.5 pounds per cubic foot. 
As these weights vary from each other less than one-third of one 
per cent., the difference is insignificant in practical problems where 
the errors and uncertainties are often large. In the further discus- 
sion of this subject, therefore, the weight of 62.5 pounds is used as 
the most convenient in calculation. 

Steam Power. The unit of steam power in ordinary use is the 
pound of steam, its pressure, and rate of use. It is, however, based 
on the heat unit, and must be so considered for detailed examina- 
tion. 

Definite quantities of work are also designated by the **horse 
power hour," equivalent to 1,980,000 foot pounds, and the "kilowatt 
hour," equivalent to 2,654,150 foot pounds. 

The pound of steam may be considered as containing an aver- 
age of 1,000 British thermal units, which may be utilized for power. 
This is equivalent to 778,000 foot pounds. 

35. Conversion of Energy Units. — The various forms of energy 
as expressed by the units named are convertible one into another in 
certain definite ratios which have been determined by the most 
careful laboratory methods. In considering these ratios, however, 
it must be remembered that, as shown in the preceding examples, 
in the transformation from one form of energy into another the 
ratios given cannot be attained in practice on account of losses 
wliich can not be practically obviated. Such losses must be, in 
good practice, reduced to a minimum, and the ratios given are, 
therefore, the end or aim toward which good practice strives to at- 
tain as nearly as practicable when all conditions and facts are duly 
considered. 

Energy must be considered in two conditions as well as in the 
above named forms, viz.: passive and active or potential and 
kinetic 

Potential energy is energy stored and does not necessarily in- 
volve the idea of work. Kinetic energy is energy in action and 



34 Power. 

involves the idea of work done or power exerted and for its meas- 
urement must be considered in relation to time. 

The most common units of potential energy and their equiva- 
lents are as follows: 
The footpound (one pound raised one foot). 

=1/62.5 or .016 foot cubic foot (of water), 
=1/8.34 or .12 foot gallon (of water). 
=1/2655.4 or .0003766 volt coulombs. 
=1/778 or .001285 British thermal units. 
The foot cubic foot (one cubic foot of water raised one foot). 
=62.5 foot pounds. 
:=7.48 foot gallons. 
=.08 British thermal units. 
=.02353 volt coulombs. 
The foot gallon (one gallon of water raised one foot) 
s=8.34 ^^^^ pounds. 
=.01072 British thermal units 
=.00314 volt coulombs. 
=.1334 foot cubic feet. 
The volt coulomb 

=2655.4 foot pounds. 
=42.486 foot cubic feet. 
=318.39 foot gallons. 
=3.414 British thermal units. 
The British thermal unit 
=778 foot pounds. 
=12.448 foot cubic feet. 
==93.28 foot gallons. 
=.2929 volt coulombs. 
Quantities of energy available, used or to be used, and eithe«" 
potential or kinetic may be measured in the above units. 

When the rate of expenditure is also stated these units express 
units of power. Some of the equivalent values of power are as fol- 
lows, those most commonly used being printed in black-face type : 
The horse power 

=1980000 foot potinds per hour. 
=33000 foot pounds per minute. 
=550 foot pounds per second. 
=31680 foot cubic feet per hour. 
=528 foot cubic feet per minute. 



Conversion of Energy Units, 35 

=8.8 foot cubic feet per second. 
=237600 foot gallons per hour. 
=3960 foot gallons per minute. 
==66 foot gallons per second. 
^=74^ watts. 

=2545 British thermal units per hour. 

. ^=42.41 British thermal units per minute. 

=.707 British thermal units per second. 

The foot pound per minute 

=1/33000 or .0000303 horse power. 

=1/778 or .00129 British thermal units per minute; 

=.0226 watts. 

=i/8.34=.i2 foot gallons per minute. 

=i/62.5=.oi6 foot cubic feet per second. 

The foot cubic foot per minute 
=62.5 foot lbs. per minute. 
=i/528=.ooi89 horse power. 
=1412 watts. 

=748 foot gallons per minute. 
=.0803 British thermal units per minute. 

The foot cubic foot per second 

=3750 foot lbs. per minute. 

=62.5 foot lbs. per second. 

=i/8.8=.ii36 horse power. 

=^48.8 foot gallons per minute. 

=7.48 foot gallons per second. 

=4.820 British thermal units per minute. 

=.0803 British thermal units per second. 
Th* watt 

=44.24 ft. lbs. per minute. 

=.00134 horse power. 

=.0568 British thermal units per minute. 

=5.308 gallons feet per minute. 

•=.7089 ft cu. ft. per minute. 

Thf British thermal units per minute 
^78 ft. lbs. per minute. 
^=.02357 horse power. 
=17.58 watts. 
=93.28 ft gal. per minute. 
=12.48 ft. cu. ft per minute. 



36 Power. 

26. Motion in General — In moving a body against a given force or 
resistance the work done in foot pounds is the product of the space 
passed through (in feet) and the resistance (in pounds). Thus in 
raising a ten-pound weight 100 feet high, 1,000 foot-pounds of work 
is performed. But this is not the only work performed. To pro- 
duce motion in a body or to bring a body to a state of rest neces- 
sitates a transfer of energy. For all moving bodies are endowed 
with kinetic energy — the energy of motion — and this energy must 
be given to them to produce motion, and must be taken from them 
to produce a state of rest. 

Hence, Newton's laws of motion: 

1. "Every body continues in a state of rest, or of uniform mo- 

tion in a straight line except in so far as it may be com- 
pelled by impressed forces to change that state." 

2. "Change of motion is proportional to the impressed force 

and takes place in the direction of the straight line in 
which the force acts." 

3. "To every action there is always an equal and contrary reac- 

tion." 

The acceleration of gravity is the acceleration due to the weight 
of a body acting on its mass. 

The weight of a body W (on account of centrifugal effect of the 
earth's revolution) varies, being least at the equator and greatest 
at the poles. From Newton's second law it follows that the accel- 
eration in motion designated by g and caused by the weight of any 
body acting on its mass will be proportional to its weight, i. e., g^= 
constant X W, and hence the weight of a body divided by the ac- 
celeration will always be constant. This constant quotent desig- 
nated by the letter M is termed the mass of the body. 

(.)M=:^ 

Let W=The weight of a body. 
M=Mass. 
g^=Acceleration due to gravity=velocity of a falling body at 

end of first second, and is ordinarily taken as 32.2 ft. 

per sec. per sec. 
A=Acceleration of moving body=velocity of body at end 

of first second. 
W'^=Weight acting. 
W"=Weight acted on. 



Kinetic Energy. 37 

V=Velocity at end of time L 

Va=Average velocity. 

t?=Time force has acted. 

S=Space passed through. 

h=Height passed through by falling body. 

V'=Initial velocity. 

S'=Initial space passed through. 

27. Uniform Motion. — In uniform motion the moving body 
passes through equal spaces in any equal divisions of time. 

Hence by definition : 

The space passed through (S) equals the product of the velocity 
(V) and the time (t). 

(2) S=Vt 

(3) V=-| 

28. Uniformly Varied Motion. — If the velocity of a body is in- 
creased or diminished uniformly, the motion is termed uniformly 
varied motion and is termed uniformly accelerated motion in the 
first case and uniformly retarded motion in the latter case. 
In all such cases the following relations hold: 

(4) A=^g. 

(5) V=At=^g t 
(6)Va=4i 
(7)S=Vat=--=- 
(8) V=VTXs. 

With falling bodies: 

S=h. 
A=g. 
From which equation (8) becomes 

(9) V=V 2gh, ^hc well known basis of hydraulic calcu- 
lations. 

(10) Work==W h=W VV2g=-=M VV2. 

>9. Compotmd Motion. — ^\Vhen bodies are already in motion and 
additional force is applied, the following relations hold : 

(11) V=V'+At. 

(12) S=S'+V't+^ 



38 Power. 

30. Graphical Representation of the Laws of Motion. — In each 



case— 



The vertical ordinates represent velocity 

Abscissas represent time. 

Areas represent space passed through. 























SPACE 





































WNiroitM Monof* 



































^.^-.-'-^ 


a»Ace 








^^^^t*"*^ 












*\.^\ 













TIM« 
MNirOAM ACCBUCRATCO MOTION 



^ 



00*4^0UN0 MOTION - UMI^tMI-lkV ACCCkCnATCO 

>Htr** IMITIAU VCLOCiTV 



^T =s constant 
S = Vt 



V = At = ,^ gt 



W 



v. = 4^ 



S = V^t = 

V=t/2AS" 



At« 



2 " lA 



V = V + At 

At* 

8= S' + V t + ^ 



Pig. 17. — Graphical Representation of the Laws of Motive. 



31. Transformation. — ^The transformation of potential to kinetic 
energy is well illustrated by water acting upon a water wheel. The 
energy in a body is always constant whatever its form, except as 
said energy be given up to other bodies or lost and wasted in vari- 
ous ways. Consequently the sum of the potential and kinetic en- 
ergies in any body is a constant quantity unless the difference be 
accounted for by energy loss or transfer as above noted. 

Water that has fallen to sea level has lost all the energy it may 
have once possessed, its energy having been expended in perform- 
ing some kind of work. 

If, in a hydraulic plant, we have an available fall of 8.8 ft. every 
cubic foot of water falling each second should produce 350 ft. lbs. 
of work per second or one horse power. After the water has 
passed through a well designed turbine it flows sluggishly away, 
having used up nearly all its energy in the turbine to which 



Literature. 39 

It has transferred its energy. If, however, on account of bad de- 
sign the water flows away at a rapid rate, say at lo feet per second, 
the head lost, fc=vV2g i. e. h=ioV644=i-55 ft. of vertical fall. 
Under these conditions the energy due to this fall still remains in 
the water, after it has left the wheel, and is lost, the loss being 
17.8 per cenL of the original energy. 



LITERATURE. 

1. Thurston, Robert H. Conversion Tables of Weights and Measures. NeW 

York. J. Wiley ft Sons. 1883. 

2. Oldberg, Oscar. A Manual of Weights and Measures. Chicago. O. J. 

Johnson. 1887. 
8. Everett, J. D. Illustrations of the C. G. S. System of Units. New York: 
MacMillan ft Co. 1891. 

4. Anderson, William. On the Conversion of Heat into Work. Discussion 

of energy conversion. London. Whittaker & Co. 1893. 

5. Unwin, W. C. On the Development and Transmission of Power. Long- 

man ft Co. London. 1894. 

6. Oswald, Wilhelnu Manual of Physics, — Chemical Measurements. New 

York. The MacMillan Co. 1894. 

7. Peabody, Cecil H. Tables of the Properties of Saturated Steam. New 

York. J. Wiley ft Sons. 1895. 

8. Richards, Frank. Compressed Air. New York. J. Wiley ft Sons. 1895. 

9. Bolton, Reginald. Motive Powers and Their PracticaJ Selection. New 

York. Longmans, Green & Co. 1895. 

10. Holman, Silas W. Matter, Energy, Force and Work. New York*. The 

MacMillan Co. 1898. 
IL Kent, Wm. Notes of the Definition of Some Mechanical Units. Am. 

Asso. Adv. of Sci. 1898. See also Eng. News, Vol. 40, p. 348. 
U Mead, Daniel W. Commercial Transformation of Energy. Trans. 111. 

Soc. Eng. 14th report, 1899. 
U. Reeve, Sidney A. The Steam Table. New York. The MacMillan Co. 

1903. 
11 Kohlrausch, F. An Introduction to Physical Measurements. New York. 

D. Appleton & Co. 1903. 
15. Carpenter. R. C. E3xperimental Engineering. New York. John Wiley 

ft Sons. 1903. 
11 Herwig, Carl. Conversion Factors. New York. J. Wiley ft Sons. 1904. 
17. Smithsonian Institution. Physical Tables. 3d Edition. 1904. 
11 American Institute of Electrical Engineering. Report of Committee on 

Standardization. 1907. Proc. Am. Inst. E. E. Vol. 26, pp. 107&- 

llOC 



CHAPTER IIL 

HYDRAULICS. 

32. Basis of Hydraulics. — ^The science of hydraulics is an empir- 
ical, not an exact science, but is based on the exact sciences of 
hydrostatics and dynamics. Its principal laws are therefore founded 
on theory, but on account of the multitude of modifying influences 
and of our necessarily imperfect theoretical knowledge of their 
varying characters and extent, the formulas used must be derived 
.from or at least modified by observation and experience and can- 
not be founded solely on theoretical considerations. The condi- 
tions under which hydraulic laws must be applied are so varied in 
both number and kind that the application of the laws must be 
modified to suit those various conditions and for this reason their 
successful application depends largely on the practical experience 
of the engineer. 

In the following discussion the letters used will have the signifi- 
cance shown below : 

E=Energy (abstract). 

P=Horse power. 

W=Total weight of water. 

h=The total available head in feet 

hi=The velocity head. 

h2=The entrance head or influx head. 

hs=The friction head. 

q=The quantity of water (in cubic feet per second). 

w=The weight of each unit of water (cu. ft.=62.5 lbs.). 

a=Area (in square inches) against which pressure is ex- 
erted. 

s=The space (in lineal feet) through which the area moves 
under pressure. 

v=The velocity of flow (in feet per second). 

gi=Acceleration due to gravity (32.2 feet per second per sec- 
ond.) 

t=The time in seconds. 

33. Mathematical Expression for Energy. — Mechanically, energy 
is the exertion of force through space. The amount of available 



Mathematical Expression for Energy. 41 

energy of water that may be theoretically utilized is measured by 
its weight (the force available) multiplied by the available head 
(the space through which the force is to be exerted), 1. e., (i) E=: 
Wh. From this it will be noted that the energy of water is in 
direct proportion to both the head and quantity. Tliis energy may 
be exerted in three ways which may be regarded as more or less 
distinct but which are usually exercised, to some extent at least, 
in common. The exertion of this energy in the three ways men- 
tioned, expressed in terms of horse power, are as follows : 

First: By its weight which is exerted when a definite quantity 
of water passes from a higher to a lower position essentially with- 
out velocity. This method of utilization is represented by the 
equation 

^ ' 560 

Second: By the pressure of the water column on a given area 
exerted through a definite space. This method of utilization is rep- 
resented by the equation ^ 

^'^ ^ 650r" 

Third: By the momentum of the water exerted under the full 
velocity due to the head. The energy of a moving body is repre- 
sented by the formula : 

Wv» 

(4) E = ^ 

The equation for the horse power of water under motion is there- 
fore represented by the equation : 

^ ' 560 X 2g 

An analysis of these formulas will show that under any given 
conditions the theoretical power exerted will be the same in each 
case. 

34. Velocity Head (hj). — It has already been pointed out (chap- 
ter II) that energy must be expended in order to produce motion 
in any body and that the head (hj necessary to produce a ve- 
locity (v) is 

(«) K = S 

This proportion (hj/h) of the available head h has to be ex- 
pended to produce and keep in motion the flow of water. This 
teid (hi) is not necessarily lost (it has simply been converted into 



42 Hydraulics. 

kinetic energy, and it may be re-cohverted into potential energy by 
correct design or it may be utilized in some other way, as, for 
example, by pressure or impact in hydraulic motors). 

Whatever head (hx) is necessary to maintain the velocity (v)^ 
with which the water leaves the plant, will be lost to the plant. 
It is, therefore, desirable to keep v at this point as low as may be 
found practicable when other conditions are considered. 

Sudden enlargements or contractions in pipes or passages may 
wholly or partially destroy the velocity and cause the permanent 
loss of the corresponding head (hj). 

In this case an additional amount of the available head (h^) must 
be used to again generate the velocity (v) required to convey the 
water through the remainder of its course. Gradual change in the 
cross-section of all channel conduits or passages is, therefore, de- 
sirable in order that the transformation from kinetic to potential 
energy, and the reverse, shall be made without material loss. 

Not only the head (hj) but still other portions of the total avail- 
able head (h) may be lost in the channels and passages of a ma« 
chine or plant by improper design. 

35- Entrance Head. — The loss of head (hg) which occurs at en- 
trance into a raceway, pipe or passage may be called the "influac 
head." The amount of this loss differs considerably with the shape- 
and arrangement of the end of the pipe or passage. In general, the- 
influx head may be determined by the formula: 

(7) h, =1^- — 1 |-2^(Merriman*8 Hydraulics, Art. 66) 

In this formula the coefficient can be obtained from table IV, lit 
which the variations of the constant under various conditions, with 
reference to a pipe inlet, are shown, and from which it will be noted 
that its magnitude depends on the shape and arrangement of the 
inlet, 

TABLE IV. 
Arrangements of a pipe uUet with corresponding coefficients. 



Arrangement of Pipe. 


c 


^- 


A. Proiectinflf into reservoir 


.716 
.825 
.950 
.990 


.956 


B. Mouth flush with side of reservoir 


.469 
.106 


C. Bell shaped month ' ;j^°™ 


.020 







Submerged Orifices. 



43 



To find the value of h^, the value of -i- — i corresponding to the 
given conditions, is to be selected from Table IV and substituted 
in formula (7). The ordinary arrangement of suction pipes is for 

a square ended pipe to project di- 
rectly into the suction pit. In res- 
ervoirs the pipe may be flush with 
ry..'.,,'..'ym. thi^ masonry or project as in the 

,, , ^ ^^g^ ^£ suction pipes. With condi- 
tion (A) formula (7) becomes 




^ \}$ f:\/ i k\iyk ttj i^^ 



(8) 



h, = .956 



2« 





0m 




^-^ - -^ ^^ ^ 


•**>* 






' — -^— _-^ir_ ^T-- "-i: 








^2 










The value of h, can be readily 
obtained from equation (8), as it 
will be 95.6 per cent, of the veloc- 
3 ity head. 

With the mouth of the pipe flush, 
with the side of the reservoir the 
loss would be 46.9 per cent, of the 
velocity head, and with a bell 
mouth pipe the loss would be de- 
creased to from two per cent. to. 
^10.8 per cent, accoi'ding to the de- 
sign of the bell mouth entrance. 

The arrangements of inlet pipes 
as referred to in Table IV are 
^^" ^^- shown in Fig. 18. 

36. Submerged Orifices. — A similar loss is sustained in the flow 
through gates or submerged openings or in the flow past any form 
of obstruction which may be encountered by the water in its flow 
through channels, pipes or other forms of passages. Openings or 
obstructions with square edges may cause a serious loss of head 
which may, however, be reduced. 

First: By increasing the opening, thus causing a reduction in 
velocity and consequently a saving in head, or 

Second : By rounding the corners of the opening or obstruction,, 
thus causing a gradual change in velocity and a partial recovery 
of any head necessarily used for creating greater velocity through 
such passage or past such obstruction. 

But few experiments have been made on submerged orifices and 
tubes. These indicate a coefficient of about .62 for complete con- 
traction which increases to .98 or even .99 with the contraction 



44 



Hydraulics, 



completely suppressed. Certain experitucnts have recently been 
made at the hydraulic laboratory of the University of Wisconsin, 
on the discharge through orifices and tubes four feet square and of ■ 
various thicknesses or lengths and with various conditions of con- 
traction. The values of the coefficients as determined in these ex- 
periments with various losses of head and various conditions of 
entrance, are shown in Table V.* 



The FormM of Entrance and Outlet Used for the Tubes in tM &Fperimeni 

were as follows:' 

A- Entrfincej all corner 90** 

OutleL; tube projecting into wftt«r on down stream side of bolkbesuL 
a Entrance; contraction eupptet^sed on bottom. 

Outlet; ttibe projecting; into water on down stream side of bulkhead. 
b Entrance; contractioD Buppres^ied on bottoii and one side. ^ 

Outlet; tube projecting into wat«r on down stream aide of bulkhead* ^M 
C Eiiinmce; contraction sup pressed on bottom and two sides. 

Outlet; tube projecting into water on down etream side of bulkhead. 
d' Entrance; contract] on euppreseed on bottom and two eidm* 

Outlet: square cornet^ with bulkhead to sides of channel presenting J 
the return current alon^ the aides of the tube. 
d Entrance; contraction suppre^sBed on bottom, two sides and top* 

Outlet; tube projecting into water on down itream side of bulkhead. 



I 



From this tabic it will be noted that a partial suppression of con- 
traction does not always improve results, and that by complete sup- 
pression, the coefficient is greatly increased with a corresponding 
decrease in head lost. fl 

37, Friction Head (h^) — In raceways and short pipes the velocity 
head (hj) and the influx head (h^) are frequently the sources of the 
/i^eatest losses of head. In canals and pipes of considerable length 
the friction of flow may become the most serious sotirces of energy 
loss> 

The principles of flow in such channels may be considered as 
follows : 

First Principle: In any fnctionless pipe, conduit^ channel or pas-^ 
sage of any length the flow may be expressed by the formula; 



(») 



lll = ^ or T ■* V2gh 



In practice, however, we find friction is always present and a 
friction factor must be introduced in the above formula in order to 



i 



♦Prom experiments by Mr, C, B. 
tilt University of Wisconsin* 



Stewart at tlie Hrdraulle Laboratory ot 



J 



^^^ 


Friction Head. 45 ■ 


1 represent the actual conditions of practice. (9) therefore becomes: ^| 


(10 


hj=q' Z_ or ▼ » c VSgh ^^^B 




TABLE V. ^^H 


Value of the Co^Usieni 0/ Di^^arg^ for flow through horUontal mibmergoi ^^H 


lufie; 4 f^^t square, for vanous lengths, lanes of head artd forme of enfraitee ^^^| 


and ouikL 


^H 


Lo«of 


Forms 
of En- 


Length of tube, in feet ^| 














■ 


bead^b» 


tt%UQ& 


O.Sl 


0.62 


1.25 


2,60 


6.00 


10.0 


14.0 ■ 


in feet* 


and 
Ontbt 














■ 


Valne of the coefficieat, c. ^| 


.0§*. «*•»•<• 


A 




.650 


.672 


.769 
.742 


.807 
.810 


.621 


.838 H 
.848 ■ 






b 


,740 






.7139 


.S32 




.862 H 




c 


,H34 






.7139 


.875 




.690 H 




c' 














,87& ■ 




d 


.948 






,943 


.940 


.927 


,931 H 


: .10.-, 


A 


.611 


.631 


.647 


.718 


,783 


,780 


.79^ H 




a 


.636 






.698 


.771 




.801 ■ 




b 


.685 






.718 


.791 




.813 ■ 







.772 






.718 


.828 




.841 V 




c' 














M^ ^ 




d 


M2 






.911 


.899 


.892 


M% 


.IS,*,*..... 


A 
a 


,609 
.630 


,628 


.644 


.70S 
.689 


,75a 
.767 


,779 


,794 
.803 






b 


.677 






.708 


.767 




,814 




c 


.765 






.708 


.828 




.839 




c' 














.82^ 




d 


.936 






,010 


,899 


.893 


.894 


M 


A 

a 


.609 


.630 


.647 


.711 
.694 


.788 
.777 


.794 


,809 
.814^ 






b 


,678 






,711 


.796 




.8:^3 




c 


.771 






.711 


.838 




.85a 




c' 














,84^ 




d 


1 .048 






.923 


,911 


.906 


.905 


1 J5 ,, 


A 

a 


.610 
.634 


,631 


.662 


.720 
.705 


.782 
.790 


.812 


.828 






b 


.683 






.720 


.809 








e 


.779 






.720 


.854 








d 


,966 






.938 


.028 






[,» — ^ 


A 

b 
e 

d 


.014 
.639 

.689 
.788 

.9i$4 


.639 


.660 


.731 


.796 


,832 


,66a 


^^^ 



46 



Hydraulics. 



The formulas (9) and (10) represent one of the important funda- 
mental principles from which many hydraulic formulas arc de- 
veloped. 

Second Principle: In any pipe, conduit, channel or passage we 
may fairly assume: 

First: From axiomatic considerations the resistance to the flow 
of water may be regarded as directly proportional to the area of 
The surface in contact with the water. 

Second : From observed conditions the resistance is found to be 
directly proportional to the square of the velocity of flow. 

Third: Experience leads to the conclusion that the resistance to 
flow is inversely proportional to the cross-section of the stream. 

These conclusions may be expressed by the following equation: 

P . __ (Yelocity)*X area of cont-act 

"" area ot section 





Fig. 19. 



Tlie area of the surface of a channel is the product of the wetted 
section or wetted perimeter (p) times the length of the section, or» 
to p X 1. (See Fig. 19.) The velocity is represented by v and the 
cross-section by a. Hence, from the above considerations, we may 
write for the friction head : 

(11) hg = ^^-^ and by transposition v* = -— ^ 

That is to say, the square of the velocity is in direct proportion 
to the area of the section and to the friction head and inversely 
proportional to the wetted perimeter and to the length of the sec- 
tion. 

In practice it is found that there are numerous factors which 



Kutter's Formula. 47 

affect the theoretical conditions, as above set forth, which must 
therefore be modified in accordance with the conditions which ob- 
tain. In formula (11) therefore it is necessary to apply a coeffi- 
cient (c') which represents the summation of such other influences. 
The form in which this last equation is ordinarily written is 

Ordinarily this form is somewhat abbreviated by substituting for 
a/p the hydraulic radius which represents this ratio. That is to say, 

area of cross section __ a _ 
wetted perimeter ~ p ~ 

The "hydraulic radius" is also sometimes termed the "mean 
<icpth" or the "mean radius." For the ratio of the resistance head 
to the length of section the equivalent slope s is substituted. 
That is to say: 

Resistance head __ h, _ 
Length of section "* 1 "" 

With these substitutions the formula (12) assumes the final 
form of: 

(13) V = ci/rs" 

In the use of this formula three factors must be determined by 
measurement or estimate in order to derive the fourth, v, r and s 
<^ be determined experimentally or measured directly. The 
factor c is the most difficult to ascertain as it depends upon a very 
^cat variety of conditions which can only be known and appre- 
ciated by a thorough knowledge of the conditions under considera- 
tion, and by comparison of such conditions with similar observed 
conditions. Various attempts have been made to derive a formula 
which would give the value of c in accordance with the varying 
conditions. The principal formulas for the values of c are those of 
Ganguillet and Kutter and of Bazin. Ganguillet and Kutter's form- 
ula for the value of c is as follows : 

38. Kutter's Formula. — 

4i.fl + l:^ + 2:«^l 

a*) c = " 



,+(..e+<L«^)_,L- 



From this formula it will be seen that Ganguillet and Kutter as- 
sume c to vary with the slope, with the square root of the hydraulic 
^dius and with a new factor "n" which is termed the coefficient 



48 



Hydraulics. 




VELOCITY "^V -iM FEET PER SECOND 



-J 



Fig. 20. 



Kutter's Formula* 



49 




Fig. 21. 



so Hydraulics. 

of roughness. The value of this coefficient as determined by these 

experiments is as follows: 
For large pipe with the following characteristics: 

Exceptionally smooth cast iron pipe n= .Oil 

Ordinary new cast iron or wooden pipe .0125 

New riveted pipes and pipes in use .014 

Pipes in long use .019 

For open channels of uniform sections : 

For planed timber sides and bottom n= .009 

For neat cement or glazed pipe .01 

For unplaned timber xyi2 

For brick work .013 

For rubble masonry joiy 

For irregular channels of fine gravel X)2 

For canals and rivers of good section .025 

For canals and rivers with stones and weeds . . . .030 

For canals and rivers in bad order .035 

The relation of the above factors may be determined by the dia- 
grams, Figs. 20 and 21. If with a known slope and a known value 
of n (for example, let n=o.i5 and s=.ooo2, as at A, Fig. 20), a 
straight line be drawn on this diagram to the scales of the hydraulic 
radius (at B) it will show at the intersection with the scale for the 
coefficient (c) the relative value of this coefficient for these condi- 
tions, or with a known c and the known hydraulic radius and the 
given slope the value of n of a channel may be likewise determined. 
After a line has once been drawn connecting these four known 
values the velocity can be determined by drawing a line from the 
hydraulic radius scale (B) to the proper point on the scale of slope 
or hydraulic gradient at x, and then from the point of intersection 
of the line A B with the coefficient scale at x' drawing a line par- 
allel with xB which will intersect the velocity scale at the point B', 
giving the velocity (in this case equal to 1.34 ft. per second). These 
formulas only apply with accuracy where the channels or passages 
are uniform and if applied to channels or passages which are not 
uniform the sections .selected must be fairly representative. If the 
sections selected are not fairly representative the value of c or n 
determined from observations and experiments may vary consid- 
erably from the values which would otherwise be anticipated. That 
is to say, the calculations based on c and n will take into account 
irregularities in channels and other unknown or unrecognized con- 
ditions, including curves, bends and obstructions which may not 



Bazin's Formula. 



S- 







^^'■~~" 










/ 








1 




T-iei 


Baiin'fi ForiDulaior the 
T«tiie of c in the foriiuil& 
T=ci^rs iSf in Eiigjish 






/ 


/ 






1 










/ 


/ 






1 










/ 


/ 


/ 




1 










/ 


/ 


/ 




J 










/ 


/ 


/ 




/ 




" ** 




S7 










/ 


/ 




/- 


— - 




= 


rr^ 


I 




1 


f 


/ 






.5.2 + ^- 

B]=0,06forimooth plank 
or matched boards. 

niM^,16 for plauka and 

brick* 

m=0.4G for nmflonrjr, 

m=0.85 for r^ular eanh 
beds. 

m^L30 for canaU in 
good order. 




/ 


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Pig. 22. — ^Diagram For Solution of Baz!n's Formula. 



GRAPHICAL 5DLUTI 



V-VCLDCITY IN FCCT PCH ICCONQ. 

C ^EOEFFIUIENT. 

R- HYDRAULIC RADIUS LR PCCT = -^, 



■ -BINE DT BLDPC 



- Jl 



V = c V 

P- 
h-i 

VALU 1 



u 

n 





.§ .7 a 9 iQ 



V = VELD[:iTIES 




V 



F CHEZYS FORMULA 



= cv¥T 



p I 



ym BQ rccT or channel bcctidn 

rtED PCnrMCTER DF CHANNEL BCCTION IN LINEAL FEtT. 

I. IN rCET BETWEEN FDINT8 CONBIDERCO. 

IBTH OR DISTANCE. BETWEEN POINTS CDNBIOCHED. IN LINEAL FECT. 




FEET PER SECDNO 





54 Hydraulics. 

have been considered at the time the original observations were 
made. 

39. Bazin's Formula. — It has been questioned by many observers 
whether the slope of the channel has any material influence on the 
value of the coefficient c. Bazin has derived a formula based on 
his examination of this subject in which he assumes that c does not 
vary with the slope. His formula, which is intended for the calcula- 
tion of flow in open channels is shown, together with a gfraphical 
table based thereon, in Fig. 22. This figure illustrates the law of 
variation of c and is applicable in principle in a general way to all 
channels and passages. 

The graphical diagram. Fig. 23, which was prepared by the writer 
in connection with Mr. J. W. Alvord, affords a ready method of 
solving Chezy's formula (13). 

40. Efficiency of Section. — From equations (12) and (13) 

(16) q « velocity X area = va 

or q = ca|/r8~= ca^5» 

With c and s constant q varies as a|/r or as^/? — 

\p 

From this the conclusion may be drawn that other things being 
equal the maximum quantify of water will pass through any sec- 
tion of any river or other channel in which the hydraulic radius is 
a maximum or the wetted perimeter a minimum. Where a choice 
exists as to the class of material with which the channel is to be 
lined c becomes a variable and q will vary as 

ca y'r or as c ^5 — 

That is to say, under circumstances where different characters of 
lining may be used the maximum quantity will pass a given sec- 
tion with c and r maximum or with c a maximum and p a minimum 
for given a. 

41. Determination of Canal Cross-section. — ^The velocity of the 
water in any artificial channel must be limited by the class of ma- 
terial used in its construction and the head which it is found prac- 
ticable to use. As noted above the efficiency of a section is greatest 
with the value of p minimum. Therefore, the semi-circular sec- 
tion is the most advantageous cross-section that can be used in a 
channel where resistance alone is considered and when the canal 



Determination of Canal Cross-section. 



55 



IS to be lined with material which can be readily shaped into this 
form. If the canal is to be lined with stone masonry it is fre- 
quently more advantageous to make the face perpendicular and 
to place the batter of the wall at the back. Where the canal is cut 
from stone or shales which will not readily disintegrate in contact 
with the water, a slope of 90"* to 40** may be sometimes used. 
Quite steep slopes can also be used with dry masonry walls. In 
material which can be handled with pick and shovel, slopes may be 
used from i to 1.25 to i to 1.50. With artificial banks of dirt and 
gravel a less slope angle is necessary and the slope must frequently 
be made as low as one to two. 

Table VI, which is taken partially from "Uber Wasserkraft und 
Wasser Versorgungsanlagen," by Ferdinand Schlotthauer, is of 
considerable value in determining the most advantageous cross- 
section in various sections which may be adopted in the construc- 
tion of a canal. As seen in the discussion above, the most advan- 
tageous cross-section, other things being equal, is that in which the 




Fig. 24. 

wetted perimeter is a minimum or the hydraulic radius is a maxi- 
mum. The following general discussion of the relations is based 
on Fig. 24. From this figure it will be seen that 

(16) a = bd + d'cota 

(17) p = b -f- 2d cosec a 
The transposition of (17) gives 

(18) b = p — 2d coeec a 
Substituting (18) in (16) 

(19) « ss dp — 2d* coseca -f- d'cotor 
The above equation now contains the area, depth, wetted peri- 
meter and functions of the slope angle, in this case a constant. 
'Hie conditions of maximum efficiency of a canal section require 



56 Hydraulics. 

that the wetted perimeter be a minimum or what amounts to t\ 
same thing with a given wetted perimeter the area a must becon 
a maximum. The value of d which makes a the maximum is d 

termined by putting ^i^ = o 

(20) ^^ = p — 4d cosec a + 2d cota 

(21) = p — 4d cosec a + 2d cota 

(22) d = 5 

4 coseca — 2 cota 

Substituting for p its value in (17) 

,oQx J _ b -f 2d cosec a 

""4 cosec a — 2 cota 
Equation (16) transposed reads 

(24) b = ^-^y^ 

d 
Substituting this value in (23) we have 

-pk— d cota -f 2d cosec a 

(25) d = -5—^ 5—- 

4 cosec a — 2 cota 

Clearing: 

(26) 4d«co8ec a — 2d«cota = a — d*cota + 2d*co8eoa 

Transposing : 



(27) d« = 



2coseca — cota 
Transforming trigonometric functions 



(28) d« = 2 

-: cos a cosec a 

Bin a 



(29) = 2 — sin a cos a cosec a 

sin a 



(30) 
Finally. 



a sin a 
2 — cos a 



(31) d = .JI^ 



• coaa 
Equation (24) may be written 

(32) b = -g- — dcota 

Table VI is calculated from the formulas: 

(31) d = J/«"^^ 

^ \2 — COS a 



Determination of Canal Cross-section. 



57 






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58 Hydraulics. 

(32) b = -j^ — dcota 

(33) B = b + 2dcota 

(34) p = b+^ 
^ ' *^ ' sin a 

In the above, a=cross-section area ; d=depth of water in channel ; 
b=bottom width ; B=width at water level ; p=wetted perimeter ; 

c=the length of slope which is equal to -; — 

In Table VI the relation of these functions, for the slopes ordi- 
narily used in practice have been calculated as well as for the semi- 
circular section. The use of the table may be illustrated as fol- 
lows: The quantity of water which it is desired to deliver is de- 
termined by the conditions of the problem or by measurement The 
velocity to be maintained in the channel is determined by the ex- 
isting slope, the nature of material encountered, or the friction 
head which it is found desirable to maintain. The area of the 
cross-section required to carry the quantity q with velocity v is 
a=-3- After the slope angle has been selected, for the material in 
which the channel is to be constructed, the corresponding values 
may be taken out of the table from their respective columns and 
multiplied by the square root of a. The result thus obtained gives 
the desired dimensions. If, for example, we desire to carry loo 
cu. ft. of water per second in a canal at a velocity of 2 1/2 ft. per 
second at which velocity small pebbles are unaffected, and with a 
side slope of 1.5 to i, which is suitable for loose earth, has been 
decided upon, the required area of cross-section will be 100/2.5 
=40 sq. ft. The square root of 40 is 6.33. The required dimensions- 
of canal as taken from the table are 

Depth d=.689 x 6.33=4.36 ft. 

Bottom width b=.4i8 x 6.33=2.65 ft. 

Top width 6=2.485 X 6.33=15.73 ft. and 

The wetted perimeter p=2.904 x 6.33=18.38 ft 
Computation of the area from the above dimensions gives 40 sq. ft 
Hence the work has been checked. 

42. The Back Water Curve. — One of the problems which be- 
comes very important in many water power installations is the 
effect on the elevations of the stream produced by the erection of 
a dam or other obstruction therein. The back water curve can best 
be determined by the use of the simple formula of flow, equa- 
tion (13). 



Flow of Water in Pipes, 5p 

From this, as shown in equation (15) 
From this equation can be derived 

(35) h. = 2^=a^xi 

With ^^ constant, h, : h', ::^ : JBl, therefore 
(36) h/.^ h»P'<^' ^ h»>'r 

That is to say, with the quantity of water and length of section 
constant, if the coefficient remains constant the head due to any 
obstruction will vary in accordance with equation (36). 

Where the water is greatly deepened in proportion to its orig- 
inal depth the value of c will not remain constant but will vary. 
Where such is the case and where q*l is constant, under which 
condition 

The difficulties in the determination of the value of c are, of 
course, obvious, but it is believed that the back water curve can 
be closely calculated by this simple formula in which the new 
value of c is the only factor to be estimated, and where the other 
elements of the problem can be determined by actual measure- 
ments. In using this formula the original value of c under exist- 
ing condition of flow can be determined by calculation based on 
actual observation of flow under different conditions of water and 
tjie conditions of the channel under the new regimen can be 
closely estimated. New values of c can be very closely estimated 
on the basis of the values known to exist under other similar cir- 
cumstances. This method will permit of a more practical solution 
of the problem than by the use of formulas based on entirely the- 
oretical consideration of conditions which can never be approxi- 
mated in practice. 

43. Flow of Water in Pipes. — Mathematical expressions for the 
flow of water in pipes may be derived from either of the funda- 
mental hydraulic formulas 

v = ci/ra or V = c^/^ba 

Starting with the former equation, in the case of a pipe flowing 



6o Hydraulics. 

full the hydraulic radius p=-^- where d is the diameter of the pipe 
and for s we may substitute --i We then have 

(38) '=*'A^* 

In a pipe of unit length and unit diameter without friction the 
flow would be expressed by the formula 

— v» 

V = i/2gli or h = ^ 

To modify this for friction a friction factor f is introduced and the 
equation then reads: 

The friction varies directly as the length and is assumed to vary 
inversely as the diameter. Hence, for any pipe of length 1 and 
diameter d the complete equation is : 

Placing (38) and (39) equal it will be found that 

16.04 

so that the equations can be made equivalent by the proper modi- 
fications of friction factors. An extensively used formula for the 
determination of c in equation (38) is that of Darcy. It reads : 

For new pipe a = .00007726 and fi = .00009647. 
For old pipe a = .0001543 and fl = .00001291. 

These coefficients were determined from experiments on small 
pipes and therefore in the case of large pipes with high velocities 
the velocities computed by this formula are too small. 

Various modifications of the Chezy formula, having the general 
form 

(41) v = cr°8» 

have been proposed or derived from experiments. Lampes and 
Flamant's are the best known of this type. Lampes reads 

(42) v = 77.68 d0.6M gO.US 
and Flamant's 

(43) v = cd* 8* 

in which c:=76.28 for old cast iron pipe and 86.3 for new pipe. 



Flow of Water in Pipes. 



6i 




63 



Hydraulics* 



The value of c in the formula v^^cV^s may vary from 75 to 15c 
for large cast iron pipe. For riveted steel pipe the coefficient varies 
but little with velocity and diameter and at ordinary velocities 
ranges from 100 to 115, A- L, Adams gives values of c for wood 
stave pipe ranging from 100 to 170. Experiments on the Ogden 
pipe line showed average values of about 120. ^ 

An examination of the various formulas proposed for calculating' 
the flow of water in pipes will show a very wide range of results 
For example, for calculating the head lost in a four-foot new cast 
iron pipe, some of the principal formulas offered and the graphical 
solution of the same are shown by Fig, 25, From these results it 
will be seen that the data from which the formulas were derived 
are evidently obtained under widely varying conditions and that 
in the relation of such formulas for use on important work, they 
must be chosen after a careful consideration of all the elements of 
the problem, and that it is usually much better, when possible, to 
utilize the original data and obsenation along similar lines when 
such can be obtained, and derive the formula to be used instead of 
accepting one whose basis may be obscure or unknown. 

In construction %vhere pipes are short and comparatively unim- 
portant, a formula may be selected which seems to agree with the 




Flow of Water in Pipes. 



63; 




9.Ct «J0 

VBLoeirv iM rccT pir sccono 



Fig. 27. 




1.0 *.o 

vcLoeiTv IN rccT wtn second 



Fig. 28. 



I 



Hydraulics, 



elements of the problem. The formulas offered by Tutton seem 
to agree well with the actual results of expferiments and several 
diagrams based thereon are shown in the following pages* In two 
of these diagrams (Figs, 26 and 27) the limiting values are shown 
and the results obtained from any pipe of the character represented 
therein should lie between these limits depending on its condition. 
44- The Flow of Water Through Orifices.— It is found that 
water flowing through an orifice in the side of a vessel acquires, 
a velocity practically equal to that which would be acquired by ^ 
falling body in passing through a space equal to the head above 
the center of the opening, i, e.j 

(44) v= i/2iir= 8.025/E 

in which 

v=veIocity of spouting jet* 
g=acceleration of gravity=32,a- 
h^=head on opening. 
The discharge through the opening would therefore be (45) q=^* 
va^^aV^gh or practically (46) q^caV^gh where c is a coefficient 
varying with the size and shape of the orifice and with various 
other factors. 

A more accurate determination of the theory of flow through a^ 
given orifice is derived as follows: ^| 

If a thin opening is considered at a depth y be- 
low the surface the discharge through the ele-^ 
mentary section Idy would be 

(47) dq = Idjy 2^ 

Integrating this equation between the limit 










h^ and h^ we obtain the following; 



(49) 



t = IKht*— h|*)i/2g or practically 

m being the coefflcient of practical modification due to condition 
of the orifice. 

45. Flow Over Weirs. — In a weir h|=o. Hence equation (49) 
becomes 

(bQ) q=^ m(|)ll/5ih* 

in which h is the head on the crest of the weir. That is, the ver- 
tical distance from the water level above to the crest of Uie weir. 



4 



Flow Over Weirs. 



65 



^- For practical use the coefficieiit m together with the constpnts 
^E- and 2g are combined as follows: 

^H e = m |;/2g =: M ^2g afid equation (50) beooEnea 

■ (51) q = c Iht 

^m The value of m and consequently of c varies with the shape of 
Hhe weir and with other factors and must be determined experi* 
Hnentally. This has been done with weirs of many forms, both by 
^Eajiin in France and by Rafter and Williams at the Cornell hydrau- 
lic laboratory. The results of these experimental determinations 
Hpe given by Figs, 30 to 34, inclusive. These figures are reduced 
^^irectly from the diagrams of Mr Rafter in the Report of the 
Board of Engineers of Deep Waterways, 1900. 
In practice many weir formulas are in use, based on various ex- 
^periments and observations. The formula of Francis', equation- 
^f(S2). is probably the best known in this country. It is best adapted 
lo long, sharp crested weirs without end contractions. 



q = BM Ih* 




Fig, 30.— Wetr Catfficlenta for Weirs of Various Shapes. 





Fiow Over Weirs, 



67 




Fijr. 35.— Weir Ooeffidentt for We! n of Tanons 91iap««» 




•66 



Hydraulics. 



Heod 

Flf r jl' IF itr' 


on CntsT of Weir in Tecr 


i3 


^5^._^-44^^ q: 


__ .^._^^.. J^^ 


- ^ 

- - 1 




|3^f^l|t|gi^riTp-if|j^| *P| I'H \\\ ]'] \ j | 


-3 , 


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tefj^ feUwi iN^^I mI-1 \-\ l-U-R-H 


zz: 


W«f - ' ,^^::f-i ^11 


IJEEhEEEE^EEEEE^^iEEEEEEE 




1 *^ .1^ ^^^,--i_z.i-,^3H 


i^W^^ffl 


E!s±? 


lai -"z--''"z-i = = --z ^"H 


H ' IbHtttmiTf 1 


:: - 








^30 z ^_z---: 




-It 


"5^*h+j i + W'HMihHH''^L-tr(''W^ 






ntr^^^y-'lthi-.i^rrzyz-^ 






E^rEEEEEEEEEEEEEEEEEEE: 

zziz=zzziz3is;PBBJJlJ3 = C; 


!?||! = ?Ee55e!EeEEEE:EEEEE 


' 


f [Ifljlm^ 


EE;iEipipEE;iE::^::EE^EE 


^,. 


?s-=i==ii=ii=EEH!! 

0»' :""-E""Ei====±-"- 


■ 1 ■ -^ ir-i 


.., 


i«9---pl-^~— ----1— — — :^^-::: 




— t 


*7.zz-:_-Lij^44: - Ji_.i3aB 
J3W.Z--I i = i = — = ---^5^:^: 


|?!?:|||? = = *?*:?5:" = = = i 




^aMp^^^nu^ 


^i 


^s^» -z----'i?^!iiii-i=izzi: 

r^^liJJjinlllllll4t^ 


M M n r[m"H 

Jon Crast of Weir in Fo«r 


^. 



Fig. 31, — Weir CopfReienla for Welis of Various shapea. 



Flow Ov<fr Weira. 



67 



Head on Great df Weir in fiset 

g^fl y> 4fl 




Hood on Creor of Weir rn Fe«r 



Pi|E. .^,--Weir OoefRc!eTi*i for Weire of Vatinni 3hap«e* 



70 



Hydraulics, 




fir- 38— Weir CoelBcients for Wein of Vailoua Shai>M. 



Flow Over Weirs. 



71 



Head on Cresf 0/ Wetr in F««t, 




Cneat of W«r m fc^ 



fig. 34.— Weir CoemclentJ, xor Weirs ot Vaj"loufl Sllai^es^ 




I- 



lb oceompqny Report an 5|K 



1899 

US.0QARO or Engineers on deep waterwavs 

WATER SUPPLY DIVISION 

Diagram showing Ofacborqe over v/elrs wffh 
irrcqular Crests. os per Boiirv's Experirr^t r?l8 . 
in compariSQn svith Dischorqe a& per Ff5knciS'& 
Formula fiif a stiorp crested woir 




"/; 



r' r' ff ■ ■gl i?' '^"ra -^ 



^ -— ^fe — vis — rt — KB — fk >Ar-Tn! — rit — rst — cAi — iJo— ■ 



Dl^hang* in Cubic f «ei- per s 




SBCfuna of AKpvnmeflM Mm^ 



1 >»^ f"^-^*^ 


^^ 


130 ITO 


fr Hoirr f«e 173 


135 


on5Bov»rw*(r,«9foloni^ffrpnaFbot,(flQJjic Fcef par 5(scona^Appin;sqma^ 


wHQttr 


t«e 


173 


03 


130 


f/O 


9%w«e>**«Hh 


T ■ 




ao 


a A 


*« 


a^ 


' "^olT" 


■a 


I4t 


Lift 


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lEO 


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3/0 


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3^ 


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19. » 


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h »rb — wi^ — licj u'a ■ le^o n'o — sse 190 — sm "» r 5 sja — » p aJa sJ g — Wt 



Dt 0f Cf"«6+ 



n a ^tr-iiirttr Jit 



74 



Hydraulics. 



A number of different tormulas for the flow over weirs are given 
on Fig. 35 and the flow as calculated by these formulas is showi> 
on the diagram. L in these formulas represents the length of the 
weir crest which in the dimension above is represented by 1. 

Figure 36 shows graphically the results of the application of the 
value of c as given on Figs. 30 to 34 as compared with Francis 
formula. 

In small weirs the effect of end contraction and of the velocity 
of approach becomes important and corrections to the formulas 
must be applied in order to allow for those influences. 

If n==the number of end contractions and the effect of each is to 
reduce the effective length of the weir by one-tenth the head on the 
weir, equation (51) will become 



'>' 



(63) q = c(l. 

The effect of the velocity of approach, for a given quantity, is tc 
reduce the head on the weir by the velocity head. This reductioD 
is given by the formula: 



(64) 






in which v'=velocity of approach and h'==velocity head. 

TABLE VII. 
Coefficient of discharge C for use with Hamilton Smith, Jr.'s formula (56) for 
flow of water over sharp crested weirs having full contraction, 
I = length of weir. 



Effective 
h6«d=h 


.66 


i(?) 





2.6 


3 


4 


5 


7 


10 


15 


19 


.1 


.632 


.639 


.646 


.650 


.052 


.053 


.653 


.654 


.655 


.655 


.656 


.16 


.619 


.625 


.634 


.637 


.0:^ 


.K39 


.640 


.040 


.641 


.642 


.642 


.2 


.611 


.618 


.<>26 


.629 


.6:10 


.631 


.631 


.632 


.633 


.634 


.634 


.26 


.605 


.612 


.621 


.623 


.624 


.625 


.62t> 


.627 


.628 


.628 


.629 


.:^ 


.601 


.608 


.(il() 


.618 


.619 


.621 


.621 


.623 


.624 


.624 


.625 


.4 


.595 


.601 


.609 


.612 


.613 


.014 


.615 


.617 


.618 


.619 


.620 


.5 


.5<.K) 


.596 


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•••• 



Literature. 75 

To allow for the influence of velocity of approach h' must be 
added to h and equation (53; becomes 

m q = c(l~n^)(h4-hM' 

Experimental results at the hydraulic laboratory of the Uni- 
versity of Wisconsin show- that for small sharp crested weirs, with 
end contraction, the formula (56) of Hamilton Smith, Jr., is prac- 
tically correct : 

(56) q = c 1 1^2^ Ihf 

In this formula 

c?=coefficient of discharge (to be taken from Table VII), 
h=observed head on crest (H) plus correction due to velocity 
of approach. 

Variations in the forms of the crest of weirs and in the arrange- 
ment of sides and bottom of the channel of approach cause con- 
siderable variation in their discharging capacity. It is therefore 
apparent that unless the conditions closely agree with those on 
which experimental data is available that the error of calculation 
may be considerable. 

LITERATURE. 

BEFEBXNOES ON GENERAL HYDRAULICS. 

1. Francis, Jas. B. Lowell Hydraulic Experiments. New York. D. Van- 

Nostrand. 1883. 
t Panning, J. T. Hydraulic and Water Supply Engineering. New York. 

D. Van Nostrand & Ck). 1886. 

3. Smith, Hamilton, Jr. The Flow of Water Through Orifices, Dver Weirs, 

and through Open Conduits and Pipes. New York. Wiley A 
Sons. 1886. 
3a. Church, Irving P. A treatise on Hydraulics. New York, Wiley ft Sons. 

4. Welsbadi, P. J. Hydraulics and Hydraulic Motors. Translated by A, 

Jay Dubois. New York, Wiley ft Sons. 1891. 

5. Carpenter, L. G. Measurement and Division of Water. Bulletin No. 27. 

Colo. Agric. Expt. Sta.. Ft. Collins, Colo. 1894. 
€. Boyey, Henry T. A Treatise on Hydraulics. New York. Wiley ft Sons. 

1895. 
7. Merriman. Mansfield. Treatise on Hydraulics. New York. Wiley 6 

Sons. 1903. 
*• Hydrographic Manual, Water Supply and Irrigation Paper No. 94. U. S. 

G. S. 1904. 
^- Hoskins, L. M. Hydraulics. New York, Henry Holt ft Co. 1907. 

BEFEBENCES ON FLOW OF WATER IN CANALS. 

^^ Hill, A. Flow of Water in Rivers and Canals. Van. Nost Bng. Mag. 
Vol. 8, p. 118. 1870. 



Hydraulics. 



11* Ganpiniet, E. Unlfomi Motloa la CansLls and Rivera. Vau. NosL Eng. 
Mag* Vo!. 2, p. 211. 1870. 

12. Searles, W> H< Slope of Water Surface in tlie Brie Canal* Trans. Am. 

Soc. a E., Vol. C, pp. 290-296, 1S77 

13. Ellis, Tlieo, G. Flow ol Water, Eng, News, Nov. 26, 1881, Vol. 8, 

478-9. 

14. Cunnlnghaio, Allan. General DlBcnssion of Flow In Canals* Proo. In 

Clr. Eng, 18S2-E3, pp. 1-95. 
IG. Fteley, A. and Stearns, F. P. Flow of Water In Conduits. Trans. 
Soc. C. E, Vol. 12 (1883), p. 114. 

16. Mmn, P. J. Irrigation Canals and Otbar Irrigation Works and Flow 

Water In Irrigation Canals. Denver, Colo. 1892. 

17, Adamai, A. L. Diagram for Calculating Velocities, Grades and Mean 

Radii for Flumes and Ditches. Eng. News, Feb. 13, 1892. p. 157. 

18* GanguUlet, E. and Kutter, W. R. A General Formula for the Uniform 

Flow of Water In Rivers and Other Channels. Trans, by Ru 

[ dolph Herring and John Trautwine. New York, Wiley & Sons. 

1893. 

19. Bou&sinesq, H. The Gradual V&rlatloas in th© Flow of Water la Chan- 

nels of Large Section. Comptes Rendus. May 31, 1897. 

20. Bouflfilnesq, J. Expertmental Verification of the Theory of Gradually 
I Varied Flow in Open Channels. Comptes Rend us. June 14. 

1897. 
2L The New Formula of Bazln. Genie Civil, March 5, 1S9S, 

22. A New Formula by Bazin for Computing Flow of Water in Open Chan^ 

nels. Eng. News, July 14, 1893* 

23. Bazln's New Formula for Flow in Open Channels. Eng. News, 1898, Vo 

2, p. 26. 

24. A Study of a New Formula for Calculating the Discharge of Open Chan- 

nels. Ann ales des Fonts et Chaussees. 2 Trimegtre, 1898. 

25. Determination of Flow in Rivers and Canals. Zeltsclir. d Oesterr. Ing. u 

Arch. Ver., Vol 50. pp, 533^34. 1898. 

26. Swan, Chas. H. and Horton, Theo. M, Hydraulic Diagrams for the Dis 

charge of Con du its and Canals, New York, Eng. News Pub 
Co. 1899. 

27. Croathwaite, Ponsby Moore. Two Graphic Methods Applied to HydraulicI 

Calculations. EngineeHng. Loudon. July 15, lS98t 1 

38, Concerning the Conception of a Hydraulic Moment of Conduit Cross Sec^ 

tlon. ZeitscJir, fur Arch, u Ing. Vol. 4G, 1900, Heft-Ausgabe. 

Col, 402-417. 
29, Siedek, Richard. Studies of a New Formula for Estimating the VeloclTy 

of Water In Brooks and Small Channels. Zeltschr, d Oeaterr. 

Ing. und Arch. Ver, Vol. 55, pp. 98-106. 1903. J 




BErEBKNCES ON FLOW OF WATEB THROUGH Fn*ES, 

30. Francis, Jas. B. Flow Through Pipes, Trans, Am, Soc C. E, Vol, 2, 
p. 45. 1872, 

31. Danach, a G. Flow of Water In Pipes under Pressure. Trans. Ahl So< 
C. E. Vol. 7, p. 114. 1878. 

32. TVehage, H, Fnction Resistance in Pipes. Dingler's Polytechnlsrhei 
Journal. 1884, p. 89. 



I 




Literature. 77 

33. Steams» F. P. Flow of Water Throat a 48^ Pipe. Trans. Am 8oc C. 

R, Vol 14, p. 1. 1886. 

34. Mair, J. G. Flow Through Pipes at Different Temperatures. Proc. Inst 

C. E. Vol. 84, p. 424. 1886. 

35. Duane, James. Effect of Tuberculatlon on Delivery of a 48^^ Water Main. 

Tnuus. Am. Soc. C. B. 1893, p. 26. 

36. Tuttle, Geo. W. Economic Velocity of Transmission of Wlater Through 

Pipes. Eng. Rec. Sept 7, 1895. 

37. Coffin, Freeman C. The Friction in Several Pumping Mains. Eng. News, 

Feb. 20, 1896. 

38. Hawks, A. McL. Flowage Test of 14"^ Riveted Steel Main at New Wes^ 

minster, B. C. Eng. News, July 30, 1896. 
3S. Flow of Water in Wrought and Cast Iron Pipe. Am. Soc. Mech. Eng. 

Dec. 1897. 
40. Herschel, Clemens. 116 Experiments on the Carrying Capacity of Large 

Riveted Metal Conduits. New York. John Wiley & Sons. 1897. 
4t Gould, E. Sherman. The Flow of Water in Pipes. Am. Mach. Mar. 8, 

1898. 
42. Hawks, A. McL. Friction Coefficient for Riveted Steel Pipes. Proc. Am. 

Soc. C. E. Aug. 1899. 
4S. Palton, C. H. Flow of Water in Pipes. Jour. Ass'n Eng. Soc. Oct. 1899. 
4i Marx, C. D., Wing, Chas. B., and Hosklns, L. M. Experiments on the 

Flow of Water in the Six Foot Steel and Wood Pipe Line of 

the Pioneer Electric Power Company. Proc Am. Soc C. E. 

Feb., 1900; April, 1900; May, 1900. 

45. Gregory, John H. Diagram Giving Discharge of Pipes by Kutter's For- 

mula. Eng. Rec. Nov. 3, 1900. 

46. Pbnnulas for Flow In Pipe. Eng. News, 1901. Vol. II, pp. 98, 118, 332. 

476. 

47. Noble^ T. A. Flow of Water in Wood Pipes. Trans. Am. Soc C B. Vol. 

49, 1902. 
^S- Sapb, A. V. and Schoder. E. W. Experimental Study of the Resistance of 
the Flow of Water in Pipes. Proc. Am. Soc. C. B. Maj, 1903; 
Oct, 1908. 

BETEBENCES ON FLOW OF WATEB OVEB WEIBS. 

49. Pteky, A. and Steams, F. P. Flow of Water over Weirs. Trans. Am. 

Soc C. B. Vol. 12, p. 1. 1883. 

50. Francis, J. R Experiments on Submerged Weirs. Trans. Am. Soc C. 
B. Vol. 13, p. 303. 1884. 

51 Henchel, Clemens. Problem of the Submerged Weir. Trans. Am. Soc 

a B. Vol. 14, p. 189. 1885. 
52. hrestlgations on the Flow over Submerged Weirs. Zeltschr. des Ver. 

Deutsch. Ing. 1886, p. 47. 
W. Hind, R. H. Flow over Submerged Dams. Proc. Inst C. B. VoL 86, p. 

307. 1886. 
W. Kaberstroh, Chas. B. Epxerlments on the Flow of Water Through Large 

Gates and over a Wide Crest Jour. Ass'n Bng. Soc Jan., 1890, 

p. 1. 

5 



f8 



Hydraulics. 



S5. 
66. 



67* 
53. 

eo. 

6t 

ea. 

$5. 
66. 

67 

6S. 

€9. 

70. 
71. 

72. 

73, 

74. 

75. 
76. 

77. 



The Floir of Water orer Dams and Spillways, Bug. Rea Jun« f , 1900. 
Flow of Water over Sliarp Greeted Weirs, Annales des Ponta et Chaua^ 

sees. Jan, 1, 18&0; Nov., 1S91: Feb., 1894. Also Proc. Eng. Club 

of Philadelphia, Jan., IBM; July. 1S02; OcL, 1892; Apr., 1893. 
Flow over a Weir of Curved Proflle. Keltschr. d Oestarr, Ing. n AicIl 

Ver. June 2, 1906. 
Flymi, A, D. and Dyer, C. W* D. The ClppcletU Trapezoidal Weir. 

Trans. Am. Soc C. B. July, 1894, 
Warenaklold, N. Flow of Water over Rounded Crest Eng. Newi, J; 

ai. 1895* Vol. 83, p. 75. 
PrUzel, J. P. and Herachel, Clemena, Flow over Wide Horizontal Top 

Welrt, Eag. News, 1892. Vol 11, pp, 290, 440, 446: 1895, Vol. 1, 

p. 75. 
John son, T. T. and Cooley, B. S. New Experimental Data for Flow ot©? a 

Broad Crest Dam. Jour, W, Soc Engrs. Jan., 1896* 
Wide Cr^t Weirs, Bazln'e Formula. Eng. News^ 1890. Vol. I, p. 16^ 

Vol, ir, p. 577: 1896, Vol, I, p. 26. 
E:cperinient3 on Flow OTor Dams, Eng. News, 1900, P< 207* 
Hafter, Geo. W. The Flow of Water over Dama, Proc Am* Soa C- IL 

Mar,, 1900. 
Heyno H. Study of Hydraulic Coemcienta, 2eltschr. d Oesterr In^. n 

Arch. Ver Dec. 6 1900. 
Dery, Victor A, E. D, Experiments on the Measurement of Water otw 

Weira Proa Inst, G. E, Vol. 114, p. 333, 1893. 



K^ 

^ 



BEFZBEKCES Olf BACK WATI3 AKP IN THEFEBIKOI. 



d 



Wood, De Volson, Back Water la Streams as Produced by Dams. Trans, 

Am. Soc. C, E, Vol. 2, pp. 255-26L 1873, 
Hutton, W. H, Back Water Caused hy Contractions, Transu Am* Soc. C* 

m Vol. 11, pp. 212-240. 1882. 
Olllmore, Q, A. Ohsrt ruction to River Discharge by Bridge Plera, Van. 

Host, Eng. Mag, Vol. 2$, p. 441. 1882. J 

Back Water from Dams. Eng, Rec, July 9, 1892, ^ 

Ferrlday, Robert Measurements of Back Water* Eng. Newa, 1896, VoL 

n, p. 28. 

Frescolm, S. W* Back Water Caused by Bridge Piers and otber Obf^tniG' 

tlons. Jour Eng. Soc, Lehigh Univ. Feb., 1899. 
The Estimation of Damages to Power Plants from Back Water. Eag. 

Rec April 26, 1902. 
Harria, E, G., Taylor, W. D.. Ladshaw, T. B. Back Water from Dams. 

The E^ect on Meadow Lands, Eng, NewSf 1902* YoL II« 

142 and 311 
Tables for Computation of Swell on Open Water Courses* Zeltachr. 

Ardi. und Ing. Vol. 49, Cola. 268-274* 1903. 
Fllegoer, A. A New Method of Computing the Back Water Curva 

SchwelzerlBChe Bauaeltting. Aug. 22. 1903. 
Tolmaa, BreiUIav. The Computation of Back Water Curves. Oesterr, 

Wocbensohn f d Oeffent Baudienst July 1, 8, 1905. 



ms. 

I 




CHAPTER IV. 

WATER POWER, 

THE STUDY OF THE POWER OF A STREAM AS AFFECTED BY FLOW. 

46. Source of Water Power. — ^Water power depends primarily 
on the flow of the stream that is being considered for power pur- 
poseSy and on the head that can be developed and utilized at the 
site proposed for the power plant. Both head and flow are essen- 
tial for the development of water power, but both are variable 
quantities which are seldom constant for two consecutive days at 
any point in any stream. The variations in head and flow radically 
affect the power that can be generated by a plant installed fdr 
power purposes. These variations also greatly affect the power 
that can be economically developed from a stream at any locality. 
The accurate determination of both head and flow therefore be- 
comes very important in considering water power installations and 
hence should receive the careful consideration of the engineer. The 
neglect of a proper consideration of either or both of these factors 
has frequently been fatal to the most complete success of water 
power projects. 

47. Factors of Stream Flow. — ^The quantity of water flowing in a 
stream at any time, which is more briefly termed "stream flow" 
or "nm-off," depends primarily upon the rainfall. It is, however, 
mfluenced by many other elements and conditions. It depends not 
only upon the total quantity of the yearly rainfall on the drainage 
area, but also on the intensity and distribution of the rainfall 
throughout the year. In addition to these factors the geological 
structure of the drainage area, the topographical features, the sur- 
face area of the catchment basin, the temperature, the barometric 
condition, all influence and modify the run-off. Sufficient data is 
not available for a full understanding of this subject, but enough 
» available so that the general principles involved can be intelli- 
gently discussed knd the problems considered in such a way as to 
?ivc a fairly satisfactory basis for practical work. A knowledge 
0^ the importance of the factors above mentioned and the extent to 
which they modify, influence or control stream flow, is essential 



Be- 



Water Power. 



to a broad knowledg^e of water power engineering. These factor? 
are discussed in more detail in chapters VI, VII and VIIL 

48, Broad Knowledge of Stream Flow Necessary. — The flow of 
a stream is constantly changing and any single measurement of 
that flow will not furnish sufficient data on which to base an in- 
telligent estimate of the extent of its possible or even probable 
economical power development* A knowledge of the economical 
possibilities of such development must be based upon a much 
broader knowledge of the variations that take place in the flow of 
the stream. In order to fully appreciate the power value of a 
stream, the character and extent of its daily fluctuations must be 
known or estimated. Averages for the year, monthly averages, and 
estimates of average power have been ordinarily taken as a basis 
for water power estimates, but they are more or less misleading, 
unsatisfactory and uncertain for the reason that such averages in- 
clude extremes, the maximum of which are often unavailable for 
water power purposes without more extensive pondage than is 
usually practicable. These maximum and minimum flows which 
affect the power of a stream not only through the quantity flowing 
but also through the head as well, as will be hereafter discussed* 
arc of the utmost importance for a broad consideration of water 
power. So also is a knowled^ife of the various stages of flow and 
the length of time that each will prevaiL Such knowledge demands 
daily observations or estimates of daily flow which can be repre- 
sented in graphical form by the hydrograph, 

49, The Hydrograph, — ^The hydrograph, constructed for the study 
of stream flow and its influence on water power, may be drawn by 
representing the daily flow in cubic feet per second at the point 
of observation by the ordinates of the diagram and the element of 
tame by the abscissas, (See Fig. 37.) The result is a graphic 
diagram which shows the character and extent of the daily fluctua 
tions in the flow of a stream at the point of observation during thi 
period for which the hydrograph has been prepared, 

A single observation of the flow of a stream represents a totally 
inadequate and unsatisfactory criterion for water power consid- 
eration. By reference to Fig, 37 it will be seen that, if the dis- 
charge of the Wisconsin River at Necedah had been measured only 
on August $t 1904, the conclusion would have been reached that 
the discharge of the river was about 2,100 cubic feet per second. 
If the measurement had been taken only on August 15, 1904, the 
flow would have been determined at about 5,850 cubic feet per 
second, or almost three times as great as on the first date, Thfl 




The Hydrograph. 



8i 



'0N033S H3d laaj otano 







I 

"8 

•I 

2 
•a 



i 



'aiiN suvntiB B3d ONoaas Hid xaaj siana m aauviaiio 

o e a a 'o 

o e a a o 

o oi ^ CD oi 

«• ^ = iV 

""-BNoaas Sad laaa "aiana n\ aaavHOiia. 



89 



Water Powtr< 



difference between the dates might be even greater, and no slng!^ 
measurement nor any series of measurements for a single week or 
month would ^ve a fair criterion from which the normal flow of 
the river could be judged. 

The hydrograph of the daily flow of a river for a single year 
gives a knowledge of the variation in flow for that year only 
under the peculiar conditions of the rainfall, the evaporation, and 
the other physical factors that modify the same and that obtain 
for that particular year. Such infonnationj while important, is noi 
altogether sufficient for the purpose of a thorough understanding 
of the availability of the stream flow for power purposes. Observa- 
tions show that stream flow varies greatly from year to yeafp and 
while, with a careful study of the influences of the various factors 
on stream flow, together with a knowledge of the past variations 
in such factors, the hydrograph for a single year may give a fairly 
clear knowledge of the variations to be expected in other years 
where conditions differ considerably, still it is desirable that the 
observations be extended for as long a period as possible. Such 
long time observations may remove the estimates of flow entirely 
irom the domains of speculation and place them on the solid ground 
of observed facts. Hydrographs of a river that cover the full range 
of conditions of rainfall, temperature, etc., which are liable to pre- 
vail on its drainage area, give a very complete knowledge of the 
flow of the stream for the purpose of the consideration of water 
power. 

It is rare, however, that observations of stream flow for a lon^ 
term of years are available at the immediate site of a proposed 
power plant. Such observations are ordinarily made only at loca- 
tions where power has been developed and where water power oi 
similar interests have been centered for a long period of time, Oc 
casionally, however, the future value of potential powers is rccog* 
nized and appreciated^ and local observations are maintained for < 
series of years by interested parties, having a sufficient knowledge 
of the subject to recognize the value and importance of such in- 
formation. The variation of flow for some considerable time pre- 
vious to construction is thus available upon which to base the desigra. . 
In considering new installations, one of four conditions obtains - 
First: Hydrographs are available at the immediate site proposed 
Second ; Hydrographs are available at some other point on tN^* 
river above or below the proposed installation. 





The Use of Local Hydrographs. 83 

Third: Hydrog^phs are not available on the river in question 
but are available on other rivers where essentially similar condi- 
tions of rainfall and stream flow prevail. 

Fourth: No hydrographs, either on the river in question or on 
other rivers of a similar character and in the immediate vicinity, 
are available. 

50. The Use of Local Hydrographs. — ^When hydrographs, con- 
structed from observations taken at the immediate site of the pro- 
posed water power installation, are obtainable, for a considerable 
number of years, the most satisfactory character of information is 
available for the consideration of a water power project. Under 
such conditions the engineer is not obliged to consider the rela- 
tion of rainfall to run-off or to speculate as to the relative value of 
the stream in question compared with other adjacent streams, or 
as to tl)e effects of the physical conditions of drainage area, evap- 
oration, temperature and other factors on stream flow. The actual 
daily flow of the stream from day to day, perhaps through all 
ranges of rainfall, temperature, evaporation and other physical con- 
ditions, is known and the principal points which must be consid- 
ered are : First, the head available ; Second, the effects of the varia- 
tions of flow on the variations in head; and Third, the extent to 
which the flow can be economically developed or utilized. Gen- 
erally, however, even where local hydrographs are available, they 
arc not sufficiently extended to cover all the variations in river flow 
which must be anticipated, and it is ordinarily desirable to com- 
pare the available data with the flow at other points on the stream 
in question or with other streams in the immediate vicinity. 

51. Use of Comparative Hydrog^phs. — Hydrographs taken at 
other points on the same river, or on other adjacent rivers where 
conditions are reasonably similar, are of great value in considering 
the local stream flow, — ^provided all modifying conditions are under- 
stood and carefully considered. Hydrographs are ordinarily pre- 
pared to show the cubic feet per second of actual flow at the 
point at which observations are made. If the observations (and 
the hydrographs based thereon) made at some other point on a 
stream, or on some other streams, are to be used for the considera- 
tion of the flow at a point where a water power plant is to be 
installed or considered, the relation of the flows at the several 
points must be determined. 

I As a basis for such comparison of stream flow, it may be as- 



Water Power. 




Wis* 



Use of Comparative Hydrographs. 85 

stream, or at points on different streams under similar circum- 
stances, is essentially the same. This is not strictly true, or per- 
haps it may be more truly said that the apparent similarity of condi- 
tions is only approximate and hence differences in results must 
necessarily follow. For a satisfactory consideration of the subject 
of comparative hydrographs, the variations from this assumption, 
as discussed in another chapter, must be understood and appre- 
ciated. For practical purposes, however, the assumption is often 
essentially correct and forms a basis for an intelligent considera- 
tion of stream flow where local hydrographs are not available. Fig. 
37 is a hydrograph constructed from observations made on the 
Wisconsin River at Necedah, Wisconsin, by the U. S. Geological 
Survey for the water year, 1904, and shows the daily rate of dis- 
charge of the Wisconsin River at that point for the year named. 
The area of the Wisconsin River (see Fig. 38) above Necedah is 
5,800 square miles. If, therefore, we draw a horizontal line from 
the point representing 5,800 cubic feet per second on the discharge 
scale (see Fig. 37), the line so drawn will represent a discharge at 
Necedah of one cubic foot per second per square mile of drainage 
area, and a similar line drawn from the 11,600 cubic foot point on 
the vertical scale will represent a discharge of two cubic feet 
per second per square mile, and so on. These lines may be fairly 
regarded not only as indicating the flow per unit of area of the 
river at Necedah, but also the relative flow per unit of area of the 
Wisconsin River at points not greatly distant therefrom. At Kil- 
l>oum, (see Fig. 38) located on the same river about forty miles 
below Necedah, the flow may be assumed to be similar and pro- 
portionate to the flow at Necedah. Above Kilboum the drainage 
2rea is 7,900 square miles, and with similar flow the discharge 
would be proportionately greater. The fact must be recognized, 
^d acknowledged, that the hydrograph is strictly applicable only 
to the point at which^ it is taken, and that certain errors will arise 
in considering its application to other points, yet observations and 
comparisons show that, while such errors exist, they are not nearly 
so important as the errors which arise from the consideration of 
averages, either annually or monthly. 

Consider, therefore, on this basis the Necedah hydrograph as 
^hown in Fig. 37. On this diagram a flow of one cubic foot per 
second per square mile at Necedah, representing an actual flow of 
5»8oo cubic feet per second at that point, would, by proportion, 
present a flow of 7,900 cubic feet per second at Kilbourn and, 



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Reliability of Comparative Hydrographs. 



8r 



with a suitable change in scale, the diagram may be redrawn to rep- 
resent the flow at Kilboum as shown in Fig. 39. This same method 
can be applied to any point on the same river or to comparative 
points on different rivers. 

S3* Reliability of Comparative Hydrographs. — It must be clearly 
understood that comparisons as above described hold good only 
as the conditions are essentially similar at the various points com- 
pared. 

Stream flow at the best is very irregular and varies greatly from 
year to year. The actual departure from the truth can best be 
imderstood and appreciated from an actual comparison of flows 
on adjacent drainage areas where observations have actually been 
made for a term of years. From such an investigation, which can 
be made as extended as desirable, the true weight to be given to the 
comparative hydrograph can best be judged. It is not believed 
that the actual variations from the truth, as shown by carefully 
selected comparative hydrographs, will be any greater than the flow 
variations which actually take place from a drainage area from year 
to year under the varying conditions of rainfall and climate. This 
method, therefore, is believed to be a scientific and systematic one 
for the consideration and discussion of probable variations in stream 
flow at any given point, if its limitations and the modifying in- 
fluences known to exist on different drainage areas and under 
liferent geographical, geological and meteorological conditions are 
known and appreciated- 

53, When no Hydrographs are Available. — In a new country 
where no observations are available either on the drainage area 
under consideration or on other areas adjacent thereto, the study 
of comparative hydrographs is impossible and a different method 
ol consideration must be used. If no data are available, time must 
be taken to acquire a reasonable amount of local information which 
should include not less than one year s observation. In addition 
to such observation a study as thorough as practicable should be 
made of the geology, topography, and other physical conditions 
that prevail on the water shed. Rainfall data is commonly avail- 
able for a much greater range of time than the observations of 
stream flow. The relations of rainfall to run-off are hereafter dis- 
cussed and approximate fixed relations are shown to exist between 
them. From such relations, and from a single year s observations, 
conclusions may be drawn as to the probable variations from the 
observed flow which will occur during the years where the rainfall 



I 





Water Power. 




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The Hydrograph as a Power Curve, 89 

varies greatly from that of the year during which observations are 
available. Such conclusions are necessarily unsatisfactory, or at 
least much less satisfactory than conclusions based on actual 
stream flow. The consideration of the best information available 
on any project is the basis on which the engineer should always 
rest his conclusions, and all relations which will throw light on the 
actual conditions should be g^ven careful attention. If a water 
power plant must be immediately constructed upon a stream con- 
cerning which little or no information is available, then the risk is 
proportionately greater, and safety is obtained only by building 
in such a conservative manner that success will be assured for the 
plant installed and on plans that will permit of future extensions 
should the conditions that afterward develop warrant an extension 
of the same. 

54. The Hydrograph as a Power Curve. — ^The hydrograph, by a 
simple change in the vertical scale similar to that already consid- 
ered, may also be made to show graphically the variations in the 
power of the stream. If, for example, at Kilbourn, a constant fall of 
seventeen feet be assumed, then a flow of one cubic foot per second 
per square mile represents a total flow of 7,900 cubic feet per second, 
and this flow, under 17 foot head, will give a theoretical hydraulic 
horse power as follows : 

H.P. = :?520X17.^ 15281 

Now if a hydrograph be constructed on such a scale that the line of 
flow of one cubic foot per second per square mile will also repre- 
sent 15,261 horse power, the result will be a power hydrograph 
(sec Fig. 40), which represents the continuous (24 hours per day) 
theoretical power of the river under the conditions named. 

On account of losses in the development of power the full theoret- 
ical power of a stream cannot be developed, and hence the actual 
power that can be realized is always less than the theoretical power 
of the stream. If it is desired to consider the actual power of the 
stream on the basis of developing the same with turbines of 80 
per cent efliciency, the line representing the flow of one cubic foot 
per second per square mile will represent the actual horse power 
to an amount determined as follows : 

A rxT> _ 7900X17X .80 7900X17 -,,,^ 
^^•■^- 878 = 11 = ^^^ 

A hydrograph platted so that the line of one cubic foot per 
square mile will represent this amount, will represent the actual 



90 



Water Power 



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The Hydrograph as a Power Curve. 



91 



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92 Water Power. 

horse power of the river at Kilbourn with the wheels working with 
the efficiency and under the head named. Such a hydrograph is 
shown by Fig. 41, referred to by the left-hand scale (A). Powcr^ 
however, is not always used continuously for twenty-four hours. 
If pondage is available the night flow may be stored and utilized 
during the day. If the flow of twelve hours at night is impounded 
and used during the day under the seventeen foot head, the power 
will be double that shown on scale A, and can be represented by 
another change in scale as shown by Fig. 41, referred to scale B. 
If the flow for the fourteen hours of night is stored and utilized in 
the ten hours of day, then the hydrograph can be made by another 
change in scale to represent the ten hours power as shown by 
Fig. 42. 

The total horse power hours which are available from a stream 
for each day may be represented (either theoretically or actually) 
by multiplying the scale of continuous power by 24. The actual 
horse power available at Kilbourn under the conditions named is 
represented by scale C in Fig. 41. It will be noted that by pointing 
off one place in the figures of scale C, Fig. 41, the hydrograph will 
represent the same condition as shown in Fig. 4a. 



CHAPTER V, 



WATER POWER (Continued.) 

THE STUDY OF THE POWER OF A STREAM AS AFFECTED BY HEAD. 

55. Variations in Head. — In the previous chapter the graphical 
representation of stream flow has been considered. A method for 
the expression of the power resulting from the fluctuations of 
stream flow and under a constant head has also been shown. Ex- 
perience shows, however, that such a condition seldom if ever 
occurs. In some cases where the available head is a very large 
element of the possible power, the fluctuations may be so small 
as to be of little or no importance. In many other cases where the 
available heads are considerable, the importance of the fluctuation 
in head is comparatively small, under which condition the diagrams 
already discussed are essentially correct and are satisfactory for 
the consideration of the varying power of the stream. In power 
developments under the low heads available in many rivers, the 
fluctuation in head is almost or quite as influential on the con- 
tinuous power that may be economically developed from a stream 
wthe minimum flow of the stream itself. 

The hydraulic gradient of a stream varies with the quantity of 
Wer flowing. At times of low water the fall available in almost 
every portion of its course is greater than is necessary to assure 
^he flow between given points and frequent rapids result (see R. 
^ %• 43) which are commonly the basis for water power develop- 

rieed rrow. 

M«dium Wiatttr 
Loiv Wafmr 
•tr«oni Bad. 




Fig. 43. — ^Hydraulic Gradients of a Stream Under VarlOYiB Conditions 

of Flow. 
• 



94 



Water Power. 



ments. As the flow increases, however, a higher gradient anc 
greater stream section is necessary in order to pass the greater 
quantity of water, and the rapids and small falls gradually become 
obscured (as shown by the medium water lines, Fig. 43) or dis- 
appear entirely under the larger flows (as shown by the higher 
water linei Fig. 43) • Water power dams concentrate the fall of the 




Ftg. 44. — Hydraulic Gradients of the Same Stream After the ConBtnietloii 
Dam and Under Various Conditions of Flow. 



tlon of™ 



J 



river that is unnecessary to produce flow during conditions of lo' 
and moderate water (as shown in Fig, 44), and when the gradient 
of the water surface and the cross section of the stream are tn- 
^ creased to accommodate the larger flow, the fall at such dams is 
frequently greatly reduced (as shown by the medium water line In 
Fig. 44) or, during high water, the fall is largely or completely de- 
stroyed (as shown by the high water lines in the Figtire), or at 
least is so reduced as to be of little or no avail under practical water 
power conditions. M 

The cross section of the river bed, its physical character ana 
longitudinal slope, are the factors which determine the hydraulic 
gradient of a stream under different flows* They are so variable 
in character and their detail condition is so difiicult of determina- 
tion that sufficient know^ledge is seldom available, except possibly 
in the case of some artificial channels, to determine, with reason- 
able accuracy, the change of the surface gradient and cross section 
of the water under various conditions of flow. Where a power pi 
is to be installed, it is important to ascertain the relation of floi 
to head in order that the available power may be accurately detei 
mined. Where a river is in such condition as to make the &i 
termination of a discharge rating curve possible, either by din 
river measurement at the point in question or by a comparison wi 
the flow over weirs at some other point, such determination shoul 
be carefully made, as such knowledge is of the utmost importain 
in considering the problem of continuous power. 



The Rating Curve, 



95 



S6. The Rating or Discharge Curve, — The rating curve, which 
will be discussed in some detail in a later chapter, is a hydrograph 
that represents the relation of the elevation of the v;^ater surface in a 
channel to the quantity of water passing a given cross section. The 
form of this curve varies with the various conditions of the cross 
section both at the immediate point and for a considerable distance 
above and below the location considered and can usually be de- 
termined only by detail observations. The rating curve is a uni- 
form curve only for channels in which no radical change in form of 
cross section occurs with the increase of fiow. (See A Fig. 45.) If, 
on account of o%^erflow conditions, or sudden enlargements of the 
cross section, that cross section varies radically in form at a given 
height, then at this elevation a radical change in the slope of the 
rating curve is likely to occur. (See B and C Fig, 45,) 






m 






Ftg, 45. — Tte Influence of the Stream Cross Section on the Rating Curve. 

Any change in the bed of the stream may, and frequently does, 
modify to a considerable extent the rating curve, which must be 
expected to vary under such conditions to an extent that depends 
on the variations that take place in the cross section and elevation 
of the stream bed. Such variations, however, are not, as a rule, of 
great magnitude and consequently will not usually affect the head 
materially at a given point. 



k-^ 



96 



Water Power* 



In Fig, 46, which shows the rating curve of the Wisconsin Rin 
at Necedah, Wis., as determined at different times during the years 
1903 and 1904, an extreme change of head of about six inches will 
be noted for ordinary flows. When tlie change in head is of s 



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Fig. 46. — Eating CurTes^ Wisconsin River at Necedah, Wla*, Showing Ch; 
in Head Due to Changes In Cross Section. 



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ficient importance to warrant the expense, the river channel may b^ 
so dredged out as to restore the original head when the reduction 
in head is occasioned by the filling of the section* ^ 

57. The Tail Water Curve. — It will be readily seen that while the 
rating curve sliows the relation between stream flow and river 
height prior to the construction of a dam, it will still represent the 
condition of flow below the dam after construction is completed. 
The water flowing over the dam will create a disturbed condition 
immediately below. If the velocity of the flow is partially checked , 
or entirely destroyed, a heading-up of the water may result beloi^fl 
the dam suflicicnt to give the velocity required to produce the iow^ 
in the river below, but it will soon reach a normal condition similar^ 
to that which existed previous to the construction of the dam* 

58* The Head Water Curve, — In Chapter III is shown (see Fi| 
35 and 36) the discharge curves over weirs of various forms and lh( 
formulas representing them are also quite fully discussed, Froi 



The Graphic Representation of Head. 



97 



these formulas or diagrams a discharge curve can be readily cal- 
culated, with reasonable exactness, for a dam with a certain form 
and length of crest. Such a curve will show the height of the head 
waters above the dam and under any assumed conditions of flow. 
From the rating curve of the river at the point considered, and the 
discharge curve of the weir proposed, the relative positions of head 
and tail waters under varying conditions of discharge can be readily 
and accurately determined, and if a weir is to be built to a certain 
fixed height, it will be seen that the head under any given conditions 
of flow may be thus determined. 

59. Graphic Representation of Head. — Fig. 47 shows the rating 
curve of the Wisconsin River (see lower curve marked "Tail Water 



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OISCHARBC IN CUBIC rtlT PER SeOONO 

Tig. 47.--Showing Head at the Kilboum Dam Under Various Conditions of 

Flow. 



Water Power, 



I Curve") at Kilboum. On this diagram has also been platted scv- 

■ eral discharge curves^ two being for a weir of 300 feet in lengtb 
I and two for a weir of 350 feet in length* Both weir curves in the 
I upper set are based on the assumption that the entire flow of water — 
I is passing over the weir. The crest of the dam is shown as raise^| 

■ to gauge 19, and the distance between the rating curve, which now 
m represents the height of the tail water, and the weir discharge 

■ curves, which represent the height of the head water (with two dif- 

■ ferent lengths of weir) under different conditions of flow, wilt show 
I the heads that obtain at all times under these assumptions. 
I The entire discharge of the stream, however, will not pass over 
I the dam except when the plant is entirely shut down, which wouhl 
I seldom be the case. The essential information which is desired 
I therefore is the available head when the plant is in active operation. 

■ At the Kilbourn plant the discharge of the turbines to be installed 

■ under full head will be 7,000 cubic feet per second, hence, with the 
I plant in full operation, this quantity of water will be passing 
I through the wheels. Therefore in determining the relation between 
I head water and tail water it must be considered that with a flow of 
I 7»ooo cubic feet per second, the water surface above the dam will 
I be at the elevation of its crest, no flow occurring over the spillway, 

■ and that only the flows greater than this amount will pass over 
I the dam. Another curve for each weir has therefore been added 
I to the diagram in which the zero of the weir curves is platted 
I from the point where the line representing the height of the dam 
I (elevation 19) intersects the line representing a discharge of 7,000 
I cubic feet per second. From this diagram (Fig. 47) it will be seen 
I that other heads, shown in Table VIII, will obtain under variou 
I conditions of flow. 
I It will readily be seen that the line representing the height 

■ the dam is not essential and that the curves may be platted relative 
I to each other, leaving the height of the dam out of the question 

entirely and indeterminate. A curve constructed on this basis but 
otherwise drawn in the same manner as in Fig. 47, is shown in Fi^_ 
48. In Fig. 48, wherever the weir or head water curves pass abovfl 
the tail water curve, it shows that an increase in the head will re- 

Lsult under the corresponding condition of flow and wherever they 
pass below such curve, it shows that a decrease in the head will 
result under the corresponding condition of flow, the amount of 
which is clearly shown by the scale of the diagram- Consequently, 
: 



y 



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J 



The Graphic Representation of Head. 



99 



of, no discharge, the head available under any other condition can 
be immediately determined from the diagram. 

From this diagram the changes in head (as shown in table IX) 
can be determined and these, with a 17 foot dam, will give the total 

TABLE VIII. 

Oauge heightM and heada available at Kilboum Dam under varioue conditions 

of flow, teith a length of ttpillway ofSOO and SSOfeet 





Hkad Water 


Tail 
Water. 


Head with 


Flow in cabic feei 
per second. 


300 
ft. dam. 


a^o 

ft. dam. 


300 
ft. dam. 


350 
ft. dam. 


7000 


10 

23.9 

25.2 

27 

28.5 

30.2 

31.5 

32.7 


19 

22.3 

24.6 

26.2 

27.7 

29.3 

30.4 

31.6 


2 

6.1 

8 

10.3 
12.2 
13.6 
14.7 
15.6 


17 

17.8 

17.2 

16.7 

16.5 

16.6 

16.8 

17.1 


17 


14000 


17 2 


21000 


16.6 


28000 


15.9 


35000 


15.5 


42000 


16.7 


tfOOO 


15.7 


56000 


15.8 








heads available under various conditions of flow as shown in the 
last two columns. These heads will be seen to correspond with the 
heads given in table VIII. 



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•II8MAI6C fr WlfCOMIN RIVCR AT KILIOORN —IN CUIIC FT. PCR 8CC. 
FIc- 48. — Showing Change in Head at Kilboum Dam Under Various Condi- 
tions of Flow. 



6:J24;j? 



lOO 



Water Power. 



TABLE IX. 

Vhangev in heafi at Kilbourn D^m trifh lengths of crest ^/ SDO and S50 feet owrf 
under isarious conditionM of flow vnth result in ff total available head with 17 ft. 
dam. 





CflAXtifift IN 


HiiAD WITH 


TotAL Head with 


Flow in cubic feet 
per eecoQd. 


300 
(t. dam. 


350 
ft. dam. 


300 
ft. dam. 


350 
ft. dam. , 


7000 , 



+ ,8 
+ .2 

— .3 

— .5 

— ,4 

— ,2 
+ .1 



+ .2 
— A 
— l.l 
—1.6 
—1.3 
—1-3 
—1.2 


17 

17.8 

17.2 

16.7 

16.6 

16.6 

16,8 

17.1 


17 


14000 


17.2 


210t)0 


16.6 


mjoo 


15*9 


350UO, ..* , 


16 6 


42000 **.***. 


15.7 i 


49000...... 


15,7 ' 


66000 - 


15.8 







I 



60. Effects of Design of Dam on Head. — It should be noted in 
both of the last diagrams that the height of the water above the 

dam is readily controlled by a change in the form and length of 
the weir; that a contraction in the weir length produces a corre* 
sponding rise in the head waters as the flow increaseSp while the 
lengthening of the weir will reduce the height of the head water 
under all conditions of flow. The physical conditions relative to 
overflow above the dam will control the point to which the head 
waters may be permitted to rise and will modify the length and the 
construction of the dam. Where the overflow must be limited, the 
waters^ during flood times, must he controlled either by a suffi- 
cient length of spillway or by a temporary or permanent reduction 
in the height of the dam such as the removal of flash boards, the 
opening of gates, or by some form of movable dam, ■ 

- Having determined the head available at all conditions of river 
flow, the hydrograph, as previously shown, may be modified to show 
the actual power of the river under the varying conditions of flow- 
The vertical scalei in this case, instead of being uniform must be 
variable as the head varies. Fig. 49 shows graphically the variation 
in the continuous theoretical power of the river taking into con- 
sideration the variation in head which wtll actually occur* Com- 
pare this hydrograph with Fig. 40 in which no variation in head 
IS considered. ^| 

61. Effect of Head on the Power of the Plant — ^It is important^ 
at this point to take into consideration the effect of head and fiow^ 
on the actual power of the plant. In most rivers^ under flood coj 




EfiEects of Design of Dam on Head. 



lOI 



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Water Power, 



tions, the power theoretically available is largely increased, forJH 
while the head may diminish, the flow becomes so much greater 
that the effect of head on the theoretical power is more than off- 
set thereby. Practically; however, the conditions of head under 
which a given water wheel will operate satisfactorily (L e. at afl 
flxed speed) are limited, and, while the theoretical power of the 
river may radically increase, the power of the plant installed under 
such conditions will often seriously decrease, and under extreme 
conditions may cease entirely. The discharging capacity of any 
opening is directly proportional to the square root of the head, andl 
the water wheel, or water wheels, simply offers a particular fornlfl 
of opening, or openings, and operates essentially under this general 
law» With a fixed efficiency, therefore, the power which may be 
dereloped by a water wheel is in direct proportion to its discharging 
capacity and to the available head. Hence, the power of the wheel 
decreases as the product of these two factors, and therefore the 
power available under conditions of high flow and small head are 
much less than where the head is large and the total flow of the 
river is less. The only way, therefore, to take advantage of the 
large increase in theoretical power during the high water condi- 
tions is to install a surplus of power for the condition of average 
water. This may sometimes be done to advantage, but its extent 
soon reaches a practical limitation on account of the expense. ItH 
often becomes desirable to take care of such extraordinary condition 
by the use of supplemental or auxiliary power. Such power can^ 
usually also be applied during conditions of low water flow whe 
the power is limited by the other extreme of insufficient water undc 
maximum head. 

In considering the effect of head on the power of a plants it is 
necessary to understand that water wheels are almost invariably 
selected to run at a certain definite speed for a given power plant 
and cannot be used satisfactorily unless this speed can be main- 
tained. Also that any wheel will give its best efRciency at a fixed 
speed only under limited changes in head. If the head change 

L radically, the efficiency changes as well and this fact become 
more serious imder a reduction in head. As the head is reduced/ 
the discharging capacity of the wheel and its efficiency is also^ 
rapidly reduced so that the power of the wheel decreases moii 
rapidly than the reduction in the diseharj^^in^ capacity would 
indicate. When the reduction of head reaches a certain point thi 
wheel is able to simply maintain its speed without developinf 



I 



can 

: IS 

bly 

ant 

in- 

cei^B 

?4 

ed, 
Iso^ 

ulfl 

thm 

Of 

1 



Relations of Power, Head and Flow. 103 

power, and when the head falls below that point, the speed can no 
longer be maintained. It is therefore plain that when the head of 
a stream varies greatly, it becomes an important and difficult matter 
to select wheels which will operate satisfactorily under such varia- 
tions, and, when the variations become too great, it may be prac- 
tically or financially impossible to do so. This subject is discussed 
at length in a later chapter, but is called to the attention of the 
engineer as an important matter in connection with the study of 
head. 

6a. Gcaphkal InvisstigatiMi of die Rdations of P o wer, Head and 
Flow. — ^The relation of head and flow to the horse power of any 
stream on which a dam has been constructed, may be graphically 
investigated and determined by a diagram similar to Fig. 50. On 
this diagram are platted hyperbolic lines marked "horse power 
curves" which show the relation of horse power to head and flow 
within the probable limits of the conditions at Three Rivers, Mich. 
These Knes are drawn to represent the actual horse power of a 
stream under limited variations in head and flow and on the basis 
of a plant eflBLciency of 75 per cent. These heads, which actually 
obtain at the Three Rivers dam, were observed under three condi- 
tions of flow, and these observations were platted on the diagram 
at c e e and a curve was drawn through them. From the intersec- 
tion of this curve with the horse power curves, the actual power 
of the river available tinder the actual variations of head and flow, 
is determined. These measurements were taken with all of the 
water passing over the dam. 

Let us assume that it is desired to investigate the eflFect of an 
installation of wheels, using 600 cubic feet per second, under a 
nine foot head. Under these conditions part of the water will pass 
thim^ the turbines instead of over the crest of the dam, the 
available head will therefore be somewhat reduced, and the power 
curve of the river, under these new conditions, is shown on the 
diagram by the curve f f f. This curve was platted from the curve 
c c e by computing the amount the head on the crest of the 
dam would be lowered at different stages of the river by diverting 
throogh the wheels the quantity of water which they will pass under 
the reduced head. The actual power of the river at different heads 
and nnder these conditions is shown by the intersection of the line 
fff with the horse power curve, and the actual power of the pro- 
posed plant under various conditions of flow is obtained by pro- 



104 



Water Power. 




I 



8.5 S.O 9.5 ID.Q IQ5 

TOTAL FALL FROM ABOVE DAM TD MOUTH Qr TAlk RACE 
Fig, 60.— Graphical Study of Head 

'Ejecting the point of intersection of the discharge line with the 
line f f f on the turbine discharge line d d. 

Thus, with a flow of 6oo cubic feet per second^ the power of the 
plant would be about 470 horse power, while, with a flow of 
2 J 00 feet per second, the power of the plant would decrease to about 
420 horse power. At discharges below 600 cubic feet per second, 
the head would drop rapidly unless a portion of the installation was 
shut down* 

63, Graphical Study of Power at Kilboum. — A more detailed 



I 



• 



Relations of Power, Head and Flow. 



105 



S3»lkaH|Tl «ZS^^» INVliI iO UiMDd 1V3I13U01H1 



T I 



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oisoia S31V3 nv 

s g 



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* ONOoas usd laaj oiano ni aabVHOsio 






io6 



Water Power. 



study of head in connection with the conditions at Kilbourn, Wis- 
consin, is illustrated by Figures 51 and 52. In Figure 51 the theo- 
retical horse power of any stream resulting from any variation be- 
tween the head and flow is shown by the hyperbolic curves drawn 
from the upper to the right hand side of the diagram. Figure 47* 
already considered, shows the relation of the head and tail water at 
Kilbourn, where a dam with a crest 350 feet in length is projected. 

The curve on Figure 51 marked '* Height of crest of dam above 
tail water** was obtained by subtracting the height of tail water 
at the various river stages, as given by the rating curve of the 
river, from the height to which the dam is to be constructed and 
platting the same in their correct position on the diagram. The 
dam here considered is 17 feet in height above average water or 
with its crest at elevation 19 on the gauge. The curve on the right 
marked "Fall over dam, — all gates closed*', is constructed in the 
same manner by laying off as abscissas the actual head as deter- 
mined from Fig, 47 under various conditions of flow when the 
whole discharge of the river is passing over the dam. The ab- 
scissas, therefore, between these two curves show the head on 
the crest of the dam when the whole discharge of the river is 
passing over the dam. For any given river discharge (as for in^V 
stance 16,000 cubic feet per second) the total fall can be obtained 
tin this case 18.8) and the theoretical horse power of the river (in 
this case 34,000 horse powder) can be determined by finding the 
intersection of the line for 16,000 cubic feet per second with the 
curv^e marked "Fall over dam, — all gates closed*', and determining 
the relation of this point to the power curves. This relation is 
more clearly indicated by the first scale to the right. 

64. Power of the Kilboum Wheels Under Variations in Flow* — 
When the gates to the turbines are open a less quantity of water 
will flow over the dam and the head on the crest w^ill therefore be 
diminished. The amount of w^ater which will pass through the pro- 
posed installation under various heads, is shown by the curve 
marked "Discharge 24-57" turbines/* The intersection of this cun-e* 
with the discharge lines, at all points to the left of the curve marked 
''Height of crest of dam above tail water** indicates that such flows 
will pass through the wheels at the head indicated by the point of 
intersection. The practical limit of the turbine capacity is the 
discharge indicated by the point of intersection of the turbine 
discharge curve with the '^Height of crest of dam above tail water". 
It will be noted that this intersection shows a maximum discharge 



J 



Effects of Low Water Flow, 107 

of 7fiCO cubic feet per second under a head of 17 feet. A further 
increase in the discharge of the river up to 8,700 cubic feet per sec- 
ond, causes an increase in the head, which is found by following 
upward the curve marked "Head 24 turbines" to the point m where 
a maximum head is indicated. The discharge from the turbines 
under this condition increases but slightly and is indicated by the 
vertical projection of the point of greatest head (m) on the turbine 
discharge line (at n) which is so slightly above the 7,000 cubic feet 
line as to be hardly distinguishable on the diagram. 

The power of the plant depends upon the head and the discharge 
through the wheels, hence the theoretical power which might be 
developed by the 24 turbines with a flow of 8,700 cubic feet per 
second would be about 13,800 horse power, which can be deter- 
mined by calculation or is shown by the relation of the point n to 
the power curves. The actual value of these various points is more 
clearly shown on the second scale to the right, marked "Theoretical 
power oi plant 24-5/' turbines". A further increase in the dis- 
charge decreases the head until for the 24 turbines a minimum is 
reached at a discharge of 42,500 cubic feet per second. Under this 
condition of head the discharge through the wheels has also been 
somewhat reduced, and the corresponding horse power is reduced 
to 11,300 as shown by the intersection of the discharge curve and 
the line indicating the head existing under these conditions. 

65. Effects of Low Water Flow. — In the case of low water when 
the flow is not sufficient to maintain the flow over the dam, if the 
turbines are run at full capacity, the water level behind the dam 
will drop until a point of equilibrium is attained where the head is 
just sufficient to force the entire discharge through the turbines. 
As the water level is lowered below the crest,^ the power of the plant 
rapidly diminishes owing to the great decrease in the head for a 
small decrease in the flow. When the head decreases beyond a 
certain point the power of the plant may be increased by closing 
some of the gates of the turbines until the discharge through the 
turbines is less than the discharge of the river, v/hen the head will 
increase by the backing up of the water behind the dam. 

Thus it will be seen by the diagram that, with only 6,000 cubic feet 
per second flowing in the river, if all of the turbines are operated 
the head will drop to about 12.7 feet, and the power of the plant 
under this head and flow would be about 8,660 horse power. If, 
under these conditions, one unit of six turbines, amounting to one- 
fourth of the plant, is shut down, the water will rise until the head 



toa 



Water Power. 



is increased to about i8 feet. Under these conditions about 
cubic feet per second of this water will waste over the dam, and th 
power developed by the remaining portion of the plant will be io,6jo 
horse power, or, about 2^000 horse power more with one unit shut 
do%vn and with the resulting head than with all units in operation 
and the consequent lower head. The above discussion simply illus- 
trates the point that it is rarely desirable to draw down the head 
of an operating plant, at least to any great extent, for the sake of 
operating a greater number of wheels, unless this is done for the 
purpose of impounding the night flow for use during the day or at 
times of maximum load. Even in this case too great a redaction ^ 
in the head is undesirable and uneconomicaL ^M 

66. Effects of Number of Wheels on Head and Power, — Fig, 52" 
is an enlarged section of that part of Fig, 51 shown by the dotted 
lines. This diagram shows how the head on the wheels may be 
maintained by shutting off some of the wheels in case the flow be- 
comes so small as to entirely pass the wheels and thus reduce the 
head, as described above. It will be noted that with a total instal- 
lation of 48 wheels, by closing the gates of two wheels at a time, 
the variation in the head would be only a fraction of a foot until as 
many as 24 wheels ahe closed. Hence it will be seen that when th 
power has been decreased by a rduction of head, the wheels shoul 
be closed off until the same power can be secured by the less nura-^ 
ber of wheels operating with the highest head that is available with 
the given discharge of the river. As the lower flows of the river 
are reached great fluctuation in the head will occur with the opera* 
tion of the turbine gates. This diagram shows the actual delivered 
power of the plant and is based on a plant efBciency of 75 per cent 
The po%ver obtained for a given discharge is therefore less than 
shown by Fig, 51. 

In order to secure more accurate results a small correction f( 
the variations in efficiency under the variations in head may some 
times be desirable. In the problem under consideration this is 
unnecessary on account of the small variation which takes place. 
Howevej-, when the variations in head are considerable, this correc-^j 
tion is essential if a close estimate of power at different heads i^H 
desired. Figure 53 is a power hydrograph similar to those already" 
discussed but with such changes in the scale as to show the con- 
tinuous power that could have been developed by these four groups 
of turbines at Kilbournj Wisconsin, during the year 1904, under 



I 

Ih 1 



Effects of Number of Wheels on Head and Power 109 





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Head In Feet 

Note— H. P. Ourrefl *re based on 7S^ efficiencj 

Fig. 52. — ^Relation of Number of Wheels to Power and Head. 



^hc variations in head which would actually have occurred with the 
dan it is proposed to construct. 

From the previous discussion of the conditions at Kilboum it 
^ seen that with a dam with fixed crest the variations in head, 
due to variations in flow, are comparatively small. Consequently 
the power of the wheel to be installed will not decrease with an in- 
crease in flow to as great an extent as usually occurs in water 
power plants. If a system of flash boards or an adjustable crest is 
found desirable in order to prevent overflow at times of flood, the 
power of the plant when these are lowered will be still further 
reduced. 

* The hydrog^ph may be utilized for more detailed analysis of 
water power questions and will be further discussed in a future 
chapter. 



no 



Water Power, 



s 



o 
m 




^ 



31tlN BtiVntii Hid DflUaiS IHd 133i 311113 Ht 39lfVHlfi1C 



J 



CHAPTER VL 

RAINFALL. 

67. Importance of Rainfall Study. — The influence of rainfall on 
ihe flow of streams is so direct that those unfamiliar with the sub- 
ject are apt to assume that the relation may be represented by 
some simple expression and that, therefore, if the rainfall for a 
period of years be known, the corresponding stream flow may be 
directly and readily calculated therefrom. With only a brief famil- 
iarity with the subject it is evident that no such simple relation ex- 
ists. The relationship is, in fact, complicated by a multiplicity of 
other physical conditions which have an important if not an equal 
influence. 

Observations of stream flow are quite limited both in time and 
geographical extent while the observations of rainfall have extended 
over a long period of time and the points of observation are geo- 
graphically widely distributed. If, therefore, it is possible to trace 
such relationship between the flow of streams and the rainfall 
and other physical conditions on the drainage areas as will enable 
the engineer to calculate the flow even approximately, such relation- 
ships become of great value to the water-power engineer, on ac- 
count of the lack of other more definite information. It is there- 
fore important that the engineer inform himself as fully as pos- 
sible on the relations that exist between rainfall and stream flow 
and the modifications of those relations by other physical factors. 
By such means the information regarding rainfall, already recorded 
for long terms of years, may be applied to the problem of stream 
flow in which the engineer is more directly concerned. For this 
reason the subject of rainfall is here discussed in as much detail 
a£ the space will permit. 

68. Distribution of Rainfall. — A continuous circulation of water 
is in progress on the earth's surface. The evaporation from the 
water and moist earth surfaces rises into the atmosphere in the 



fir t?ff' 1^' 1^' KV lie* 117' 113' itr \ir 



lor JDi' lor MJT 
^0 




jlr uV tif* iil^ ir m lojr laf ioT lir wF 




"4 



Rainfall. 





lisa 



111* 





1117 



llil 





r •' 


^SL^^lI^iHiMM 



1900 



isTote Petite tiE 



|ti tn tt^^it TO nKc^i> to 4iE 



aovr* 4* 



fig. 55.— Distribution of Total Annual Ralnfitl In Wfseonmln 




Fte fit,— DfBtHbutlon of Total Ajmna! Rainfall In Wisconsin. 



ii6 



RainfalL 




form of vapor, partially visible as clouds, mist and fog, and is" 
afterwards precipitated as rain and dew* The dtstribution of rain- 
fall on the earth's surface is by no means uniform. An examina- 
tion of Fig. 54, which is a map showing the average distribution of 
the annual rainfall in the United States, will show how greatly the 
average annual rainfall differs in various parts of the United States. 
The local variation in the average annual rainfall in the United 
States is from a minimum of no rainfall, during some years in the 
desert regions, to an occasional maximum of more than one hun* 
dred inches in the extreme northwest. From this map it will be 
noted that from the Mississippi westward the lines of equal rain- 
fall are approximately north and south and parallel with the moun- 
tain ranges. In the Southern states, east of Texas, they are ap- 
proximately parallel with the Gulf of Mexico, and on both the At- 
lantic and Pacific coasts they are approximately parallel with the 
coast lines. At various points in the United States other influences 
come into play and greatly modify the genera! distribution as above 
outlined. In a general way the rainfall may be said to be in* 
fiuenced by the topography of the continent and, to a considerable 
extent, by its altitude. In general, the rainfall decreases as the 
elevation above sea level increases, although in some cases the op- 
posite effect holds. This general law seems to be substantiated by 
reference to the annual rainfall map. In passing along the parallel 
of 40* as we ascend from the Mississippi River to the western 
mountains the annual rainfall decreases from about 35 inches an* 
nually to 10 inches or less. On the other hand, a reference to our 
Western coast will show that some of the heaviest rainfalls that 
occur are due to precipitation caused by the moist winds from the 
Pacific striking the higher mountain ranges. This is a local condi- 
tion, however, and is quite different in its character from the gen* 
eral law above stated. The mountain ranges along the Pacific 
coast which intercept the moisture from the Pacific and cause the 
heavy rainfalls in the higher mountain areas are also the direct 
cause of the small rainfall in the arid regions lying east of these 
mountains, 

6g. The Painfall Must be Studied in DetaiL — ^The map of average 
annual rainfall is of value only for a general view of the subject. 
For special purposes a detail study of the local variations from the 
average conditions is necessary. Great variations take place in the 
annual rainfall of every locality. Sometimes the annual rainfall 
will be for a series of years considerably below the average, and 




DistnbuLign of Weekly Rainfall io Wisconsio. 117 





HAY 13 TO MAY 2d 



MAY ao TO MAY 27 





^UHC 3 TO JUNE 10 




JUNC 17 TO JUNE a4 



rMOHta IN DCPTH 



OTO.^' ^nVO-fiO" j»OTOta' TO'TOr ir&OVtfl 

Fig. 57.— DIstrlbntfon of Weeltly Rainfall tn Wlsconstn* 



ii8 



Raiofali. 




Fl£. &8.— RainraU Conditions In the United Statefl at S A. M.. Julf Uit, mi 





Ft£. G9.— Eatufali Condltioiui In the United States at S A. M.« Jaly 17tli, 110'^^ 




Local Variations in Annual Rainfall. 1 19 

then for a number of years the average may be considerably ex- 
ceeded. No general law seems to hold, however, in regard to this 
distribution and the variation seems to occur either without law or 
by reason of laws so complicated as to defy determination. The 
variations in the distribution of the annual rainfall in the State of 
Wisconsin for eleven years are shown by Figs. 55 and 56. From 
these maps can be clearly seen how greatly the distribution of rain- 
fall thronghout the state differs in different years from the average 
annual rainfall as shown on the last map of the series. It should 
also be noted that in the same manner these annual rainfall maps 
are the results of the summation of an irregular distribution of 
numerous rainstorms, the irregfularities of which can perhaps be 
more clearly shown by the maps on Fig. 57 which show the weekly 
distribution of rainfall in Wisconsin for six consecutive weeks in 
May and June, 1907. All such maps are but the result or sum- 
mation of individual rainstorms which occur during the period 
considered Individual rainstorms never occur twice over exactly 
the same geographical extent of territory nor with equal intensity 
at any points within the territory covered. They are not only 
irregular in their distribution but progressive in both their dis- 
tribution and intensity, changing from hour to hour during their 
occurrence. The extent of a somewhat general rainstorm in pro- 
gress at 8: 00 A. M. (Washington time) over the Northwest on July 
i6th, 1907, is shown by Fig. 58. On the area over which this storm 
extended, the actual precipitation varied widely and the extent of 
the storm rapidly changed from hour to hour. At 8 : 00 A. M. on 
July 17th the general rainfall had ceased and the storm had be- 
come localized as shown by Fig. 59. The varying character and 
extent of the rainfall as illustrated by those two maps show the 
extremes of one storm which affected the Northwest, and illustrates, 
in a general way, the irregularity and lack of uniformity in rainfall 
occurrence and distribution. 

70. Local Variation in Annual Rainfall. — By reference to Fig. 60, 
the variations which have occurred in the annual rainfall at various 
localities in the United States will be seen, and from this data the 
^2ck of uniformity in the annual rainfall will be more fully appre- 
ciated. By an examination of the records of a sufficient number 
^f years the limiting conditions may be determined and an ap- 
proximate determination of the relation between the extremely dry 
*ncl extremely wet periods made. 



X20 



RainEall. 



Si ^ 
b' iu 



ID 
fD 
40 
10 







igl 






3 



3 



Ko Atlantic, 
Hew Hiiven, Codii« 



So Atlantfc, 



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F-Afltem (Tulf, Wimti^m Gulf, Upp^r M1«Bls»lppl, l4»v&r MiinlBsf pp^ 

Moiirgo[ueT7« Al^ San Atit02}lo, Tex. Uen ^Hglnes^, l«u tiiUe itoekt Ark. 




mmmmmmMM 






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Mrri>r«headf Minn. 



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40 






























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Colorado, Great BaiiJii, 

FhoOQijc^ Arts. Wltmemuoca, N«f ^ 



60. — Variation In Annual Rainfall at Various Folate to tbe ITnlted Statat, 




Local Variations in Annual Rainfall. 



121 



Figure 6i i* a diagram showing the fluctuations that have occurred 
in the annual rainfall at Madison, Wisconsin, from 1869 to 1905. 
The variation at Madison has been from a maximum of about 
52 inches in 1881 to a minimum oi about 13 inches in 1895 which 
represents a greater range (4 to i) than ordinarily obtains. As a 
general rule the maximum may be stated to be about double the 
minimum annual rainfall. 




I 



i i i i 

riUCTUATION or ANNUAL RAINFALL AT MADISON, WIS. 

Fig. 61 

71. Local Variations in Periodical Distribution of Annual Rain- 
fall — ^The amount of the annual rainfall is only one of the elements 
that influence the run-oflF. The time of occurrence or the periodical 
distribution of the rainfall is even of greater importance. The 
general character of the periodic distribution of the annual rain- 
iall is similar each year in each locality, for the maximum and 
minimum monthly rainfalls occur in each locality at fairly definite 
periods. As the cycle of the seasons changes, conditions favorable 
or unfavorable to precipitation obtain, and, while these differ very 
largely from year to year and are subject to such wide variations 
as to render the character somewhat obscure, unless a number of 
reasons are considered, yet the same general character ordinarily 
prevails. 

Figure 62 shows the extreme and the average variation of the 
monthly rainfall at Madison. The monthly rainfall in the various 
"months differs widely in amount and is by no means proportional 
to the total annual rainfall for the year. It is especially observable 
that during the year of maximum rainfall, viz: for 1881, the rain- 
fall for April was almost as low as for the April of the year 1895 
^hen the total annual rainfall was at a minimum. It is also observ- 



RainfaU* 





VrLUCTUATiaK or MOHTHLY RAINrAlt AT MADtSOU, W19. 

Fig. 62 ■ 

able that the rainfall for August ^ 1881, was less than the rainfall for 
August of 1895. Figtirc 63 shows the typical average monthly dfe- 
tribution of precipitation at various points within the United States, 
and the general law to which even the variations mentioned par- 
tially conform. The character of the monthly distribution varies 
widely at different locations, but will be seen to have a similar 
character wherever similar conditions prevail. Thus the New Eng- 
land States present a similarity in the distribution of the monthly 
rainfall. A similarity in the montJily distribution is also fourid 
throug^hout the lake region and the Ohio Valley. The monthly dts* 
tribution throughout the Great Plains is also similar, and a marked 
similarity exists at points along the Pacific coast. 

72* Accuracy of Rainfall Maps and Records. — ^It must be under- 
stood that the rainfall maps, showing lines or belts of equal rain- 
fall, are only approximately correct, and that it would be impossible 
to show by such lines small differences in annual rainfall of less 



^ 



Monthly Distribution of Rainfall, 
lypes ef Monthly Dlstribiitkii of Predpilatioa in tk tJoited States* 



133 





124 ^^^^^^ RainfalL ^^^^^^^^^^^H 

til an two or three inches. As a matter of fact, the rainfall actually 
differs considerably within comparatively small limits, but within ^ 
such limits the average remains fairly constant for the year or sea-w 
son. Frequently, however, the rainfall variations even within 
narrow limits differ widely. Many questions of importance in con- 
nection with the consideration of rainfall are still open to debate 
and are frequently answered in a diametrically opposite manner hfM 
data secured from different localities. " 

73< Rainfall and Altitude. — ^The relation of the rainfall to al* 
titude has been a subject of frequent discussion and perhaps the 
tnajority of data secured tends to show that there is a material 
■decrease in the fall of rain as the altitude increases, and this both 
within a broad area and with great changes of altitude and within 
a limited area and where the differences in altitude are coippara- 
tively small. Mn Rafter, in the Hydrology of New York, points 
out tlie fact that in the State of New York the rainfall records 
show both increase and diminution of precipitation with increase of 
altitude. Tlie Hudson River catchment area shows a higher precipi- 
tation at the mouth of the river than it does at its source in die 
Adirondack mountains^ while the Genesee River shows the op* 
posit e : that is, a higher precipitation at its source than at its mouth. 
In this case the influence of altitude, if such influence can be said 
IQ obtain on such limited areas, is overshadowed by other predomin- 
ating influences. In this connection Fig. 64 is of interest- This 
diagram shows the variation in the annual and monthly rainfall 
at three stations within the City of Chicago, Curv« No. i shows 
the rainfall at the Auditorium Tower, at an elevation of 233 feet 
above the level of the city. Curve No. 2 shows the rainfall at the 
Chicago Opera House Building, at an elevation of 132 feet Curve 
No* 3 shows the rainfall at the Major Block, elevation 93 feet* The 
relative monthly rainfall at these three stations varies greatly, and, 
while the annual variations at these three points, — all of which are 
within a square mile in the business center of Chicago,^ — differ 
considerably from each other, still the difference is insignificant in 
-comparison with the monthly variation. While the influence of alti- 
tude may possibly be seen in the annual results and possibly in 
the monthly results as shown at stations one and three, the monthly 
results at station two show no such effect, or, at least, the effect Is^m 
greatly obscured by other inflLiences» ^ 

74- Value of Extended Rainfall Records, — ^One of the points that 
becomes important in the consideration of rainfall records is thej 



J 



Value of Extended Rainfall Records. 

JAI. PCI. MAR. APR. MAY JORC JULY A06. iCPT. OCT. ROV. OCO. 



125 



AHRRAL 
I I 3 




SO 



to 



10 



Fig. 61— Monthly and Annaal Precipitation of Three Exposures in Chicago, 
111. 1. Auditoriam Tower, Elevation 238 feet 2. Chicago Opera House 
Building, Elevation 182 feet 3. Major Block, Elevation 93 feet.* 

length of time required to make such records safe as a basis for 
future estimates. This subject is well considered in a paper by 
Alexander A. Binnie, member of The Institute of Civil Engineers, 
published in the Proceedings, Vol. 109, pages 89 to 172. Mr. 
Binnie's conclusions are that: 

"Dependence can be placed on any good record of 25 years' dura- 
tion to give a mean rainfall correctly within 2 per cent of the truth." 
Mr. Rafter, after reviewing this paper, concluded, that : 
"For records from 20 to 35 years in length the error may be 
expected to vary from 3.25 per cent down to 2 per cent, and that 
for shorter periods of 5 to 10 and 10 to 15 years the probable ex- 
treme deviation from the mean would be 15 per cent to 4.75 per 
cent respectively." 

Mr. Henry from his examination of this question in reference to 
various localities has drawn the following conclusion: 

For a ten year period the following variations from normal have 
occurred : 



KewBedford + 16percent 

Cmcinnati +20 " 

BtLonis +17 " 

Fort Leavenworth +16 " 

amFrandsco +9 " 



— 11 i)er cent 

— 17 " 

— 13 '• 

— 18 " 

— 10 " 



^Beprodnced from original slide published by Qeo]?raphical Society of Chicapro^ 



X26 



Rainfall. 



For a 23-ycar period Mr. Henry found that the extreme variation 
was 10 per cent both at St, Louis and New Bedford, and reached 
the conclusion that at least 35 to 40 years' variations are required 
to obtain a result that will not depart more than -j- or — ^5 per cent 
from true normal. The average variation of the 35-year period Mr. 
Henry found to be + or — 5 per cent and for a total 40-year period 
-|- or — 3 per cent 

75. Accuracy in Rainfall Observation.^ — It must also be under- 
stood that on account of the marked variations which actually occur 
in rainfall within limited areas and by reason of limited difference 
of elevation, the observation of actual rainfall is not without its 
difficulties. In order to secure great accuracy great care must be 
exercised in the placing of rain gauges so that they may receive 
and record the rain received in an accurate manner. Subject, as 
they are, to considerable variations, it would seem unwise to use 
great refinement in the calculations of rainfall, and in recording 
rainfall one decimal place is probably all that is warranted and 
two places is the ultimate limit of possible accuracy, fl 

76, District Rainfall, — In determining the average rainfall on zf 
drainage area an extended series of observations over the entire 
district considered become essential and conclusions drawn from 
more limited observations are subject to considerable inaccuracies. 
Rainfall stations, distributed as uniformly as possible over the 
drainage area, should be selected, and the average result of the ob- 
servations of these stations should be used as the basis of calcula- 
tion. Possibly a still more accurate method of considering this 
subject would be the selection of rainfall observations on each 
particular branch of the stream considered* The value to be given 
to each set of observations used should be in proportion to the ter- 
ritory drained by the tributaries. ■ 

77* Study of Rainfall as Affecting Run-off- — In considering the 
rainfall on a district in relation to the run-off of streams, it is 
desirable to study the rainfall records on the basis of what is 
termed "water year"* The water year for most of the area of the 
United States, instead of coinciding with the calendar year may 
be best divided into periods beginning, approximately, with De- 
cember and ending, approximately, with the foHowiog November. 
The first six months of this period, December to May inclusive, 
ts termed the "storage" period, June, July and August constitute 
ihe *'gTowing" period i September, October and November^ the **re- 
plenishing** period. For the purpose of discussing rainfall in 




Mean Monthly Rainfall. 



127 



i »! 



S3 




Kort!n*m ArTnntfc, 







61. — ^Hean Montlily EoinfalJ at ¥arioua Points fii tb« United Statea. 



ii8 



RainfalL 






* > lit 






ao 
to 


















i 




















i 








^ 


1 




dl 






Ifl 



^^sJ 









ro 












^^^kr»«^ 


^.*s 



TucsoQ, Aria. 



WlUQcoitiectt^ Her, 



Tig. 66.— Mean Monthly Rainfall at Varfaus Points In the United States. 




Rainfall oo the Drainage Area of the Wtsconsio River. 129 




l^gap^^^iiyHJ 



— lU O ^ Hi 



TOTAL 

AMfTUAL. H 



3T0RA8C 
PERIOD 



EROWINC 
PERIOO * 



iRCPLCillHlMI 

Ipcrioq. 



FIf. 67. — Hatufall on the Drainage Area of the Wlsconafn River. 



r\ 



130 Rainfall. ^^H 

relation to run-off it is desirable to divide the annual rainfall in 
accordance with these periods. Figures 65 and 66 show the average 
monthly rainfall at various points in the United States, tlie average 
rainfall for each of the periods above mentioned and an additional 
diagram for each location showing" the summation of the total rain- 
fall for each period of the water yean 

Here again attention is called to the fact that for most purposes 
of the engineer the extreme conditions and the varying conditions 
from year to year are of much greater importance than the average 
conditions as shown on these diagrams. Figure 67 shows the annual 
and periodic rainfall on the valley of the Wisconsin River at three 
different points, the relative location of which will be seen by ref- 
erence to the map on page 84. Tlie upper diagram shows the rain- 
fall on the drainage area above Merrill, the center diagram the rain- 
fall above Necedah, and the lower diagram, the rainfall above Kil* 
bourn. In these three diagrams it is important to note the variation 
in the rainfall condition above the different points on the water- 
shed. For example, considering the entire area above Kilbourn and 
above Necedah, it will be noted that the annual rainfall for 1895 
was the lowest within the period shown, while for the area above 
Merrill the rainfall for 1892 was the lowest for the period dis- 
cussed. This diagram will illustrate the fact, which is manifest on 
the investigation of most large streams, namely, that frequently 
the intensity of the rainfall upon part of the drainage area is radi- 
cally different from that on other parts, and that, consequently, the 
various quantities of rain falling on a large watershed tend to 
halance each other and keep the total more constant than observa- 
tion at any one point would seem to indicate, so that the minimum 
rainfall at any one point on the area is not necessarily coincidentj 
with the minimum rainfall that may occur at any other point o! 
on the stream as a whole. From this it is evident that in an area 
of any magnitude it is necessary to consider the rainfall at a large 
number of stations well distributed over the area. 



LITERATURE. 

OETTEEAL gtm.TECrr OF ItAI^fFALL* 



n • 

1 



4 



1. U. S. Weather Bureau. Annual Reports and Monthly Weather Re?!cT*- 

S, Meteorologfache Zeltschrlft. 

S. ZeltHchrift des Oaterreicbeti QesellacliaJt ffir Meteorologie, 

4. Symon*s Meteorological Magazine. 

B. Annuclue ds la Soclete Meteor ogique de Prance, Paris. 




Literature, 



131 



6. Th© Royal Meteorological Society of Great Britain. Quarterly JournaL 

7. Hawksley, Thomas. Laws ol Rainfall and Its UtilJzation* Proc Inst 

C. E. Vol 31p pp. 63-55. 1871. 

8. BIniile. Alei. R, Tables of Mean Annual RaJnfail in Various Parts of tb« 

World Proc Inst C. K VoL 39. pp. 27-31- 1874. 
S, Sehott, C. A. Tables and Results of tlie Preclpltatioa of Rain and Snow 
in the U, 8. Smithsonian Contribution to Knowledge, No. 223, 
1874, 
10 Charts and Tables Showing Geological Distribution of Rainfall In the 
U, S, TJ, S. Signal Service Professional Paper No. 9. 1S83. 

11. Rainfall Observatlotia at Philadelphia, Reports Phil a. Water Bureau, 

1S90-93. Eng, Record, 1891, p. 346, 1892. p, 360. 

12. Blnnle, Alex. R. Mean or Average Rainfall and the Fluctuattoua to 

which It is Subject Proc. Inst C, E, Vol, 119 (1893), pp, 
J72'1S9. 

13. Waldo, Frank, Modern Meteorology, New York, Scribner*s Sons. 1893, 
14- Davis. W, M. Elementary Meteorology, Boston. Ginn Sc Co., 1891 

15. Harrington, M, W, Rainfall and Snow of the United States. Bulletin 

C, U. S. Weather Bureau, 1S94, 
IG, RnsseU, Thomas. Meteorology, New York, MacMiUan Ca. 1895. 

17. Henry, A* J, Rainfall of the United States. Bulletin D„ U. S. Weather 

Bureau. 1897. 

18. Ttimeaure & Russell. Public Water Supplies, Chapter 4. New York, 

Wiley & Sons. 1901. 

19. Hann, Jnlltia. Handbook of Climatology, New York* M^cMiHan Co. 

1903. 

20. Handbook der Ingenleur Wissenschaften, Part 3, der Wasserbau; sec 1, 

Gewasserknnde. Leipzig. E. Engelmann, 1904. 

21. Hann, Julius, Lehrbuch der Meteerologie. Leipzig. 1906w 

EXCi:SfiIVlB BAII7FALL, 

22. Francis, Jas. B. Distribution of Rainfall during a Great Storm In New 

England In 1S69. Trans. Am. Soc, C, E, Vol. 77, p. 224. 

23. The New England Rain Storm of Feb. 10-14, 1886, Eng. News, 1886, VoL 

15, p. 216, 
24- Hoxle» R, L, Excess Ive Rainfalls Considered with Special Reference to 
Their Appearance in Populeua Districts. Trana. Am. Soc a H, 
p. 70, June, 1S9L 

25. Talbot, Arthur N, Rates of Maximum Etalnfall. Technograph, Univ. of 

Illinois. 1891-1892. 

26. Duryea. Edwin, Jr. Table of Excessive Precipitation of Rain at Chi- 

cago, Illinois, from 1889 to 1S97, Indusive, Jour. W. Soc of 
Engrs. Feb,, 1899. 

CAUSES 07 BAHTTAIX. 

27. Henry, D. F. Rainfall with Different Winds. Rept Chf, Engr. U. 8, A. 

1867, p. 598, 

28. Blanford, H. F. How Rain Is Formed. Smithsonian Report 1SS9, pt 

1, P. 2S7. 




132 Rainfall. 

29 BeJschow, Frantz A. The Causes of Rain and the Structure of the At- 
mosphere. Trans. Am. Soc. C. E. Vol. 23, p. 303. 1890. 

30. DaylB, W. M. The Causes of Rainfall. Journal of N. E. W. Wks. ABs'n. 

1901. 

31. Curtis, a. E. The Effect of Wind Currents on the Rainfall. Signal Serv- 

ice Notes No. 16. 

THE EFFECT OF ALTITUDE ON RAINFALL. 

32. Homersham, S. C. Variations of the Rainfall with the EleTation. Proc. 

Inst C. E.. Vol. 7. pp. 276. 282 & 284. 1848. 

MEASUBEMENT OF RAINFALL. 

33. Clutterbuck, J. C. Dalton's Rain-gage. Proc Inst C. E., Vol. 9, p. 157. 

1850. 

34. Fitzgerald, Desmond. Does the Wind Cause the Diminished Amount of 

Rain Collected in EHevated Rain Gages? Jour. As bo. of Ens. Soc. 
1884. 

35. Weston, E. B. The Practical Value of Self-recording Rain-gages. Bng. 

News, 1889, VoL 21, p. 399. 

36. Self-Registering Rain-gages and Their Use for Recording Ezcessiye Rain- 

falls. EUg. Rec. 1891, Vol. 23, p. 74. 

37. Duryea, Edwin, Jr. E^ffect of Wind Currents on Rainfall and <m the 

Gage Record. Signal Serrice Notes Na 16. 



CHAPTER VIL 

THE DISPOSAL OF THE RAINFALL. 

78. Factors of Disposal — ^The portion of the rainfall in which 
the water power engineer is most directly interested is that which 
runs off in the surface flow or flow of streams. In order to form 
some idea of the amount of this run-off and the factors that control 
it, it is necessary, however, to investigate and consider the various 
ways in which the rainfall is distributed, for the ways in which the 
distribution occurs are mutually inter-dependent and of necessity 
modify and control each other. The rainfall disposal depends on a 
large number of factors or conditions among the most important 
of which may be named : 

(1) The amount of the rainfall. 

(2) The rate of rainfall. 

(3) The condition of the surface on which the rainfall takes 
place. 

(4) The condition of the underlying geological strata. / 

(5) The atmospheric temperature. 

(6) The direction and velocity of the wind. 

(7) The nature and extent of vegetation. 
f8) The surface topography. 

(9) The evaporation. 

It will be noted that some of the factors mentioned above tres- 
pass more or less on others and are not clearly separable. 

79- The Rate or Intensity of Rainfall. — It will readily be recog- 
"'zed that with very heavy or intense rainfall a larger percentage 
^^ the water will run directly into the streams and a smaller per- 
centage will be taken up by the strata than would be the case were 
t^e rainfall very light. In very light rainfalls there is no run-off, 
the water being either taken directly into the strata or re-evaporated 
from the surface. 



134 Disposal of the RainialL ^^^^^^^^ 

So. Condition of Receiving Surfaces and Geological Strata.-- 
Next in importance in modifying the disposal of rainfall is the 
condition of the surface on which the rain falls and of the under- 
lying geological strata. If the geological strata are poms in na- 
ture and comparatively free from water they will readily receive 
and transmit the rainfall if the surface is in proper condition to re- 
ceive it. The condition of the surface itself modifies the reception 
of the rainfall in a very marked mannen With high surface slopes 
the rainfall may be large, even with somewhat porous strata, and 
yet very little water will be taken up by the strata. With low 
slopes and porus strata a large amount of water will be received 
directly by the surface and passed into the ground water and deep 
waters of underlying geological strata. 

The temperature has an important influence on the condition of 
the strata^ and consequently the disposal of the rainfalL Strata 
otherwise porous but with saturated and frozen surface will r^ 
ceive and retain practically no water and the consequence is that 
under these conditions even a low rainfall may produce a consider- 
able run-off that under other temperature conditions would not 
occur. 

8r, Effects of Wind — The wind has a marked effect on evapora- 
tion and consequently on the quantity of rainfall that passes away 
in the atmosphere* The average velocity of the wind will vary iti 
<]iffcrent parts of the United States from three to seventeen miles 
per hour and, other things being equal, will increase evaporation as 
such average velocity increases. 

82. Effects of Vegetation,^ — The nature and extent of the vege- 
tation on a surface has a marked effect on the disposal of the rain- 
talk Experiments at the Wisconsin Agricultural Experimental 
Station show that barley, oats and corn require 15,2, 19,6 and 26.4 
inches of rainfall, respectively, to produce a crop. This includes 
the transpiration and evaporation from the cultivated surface a^ 
well as the actual quantity used by vegetation. The amount act^ 
ually retained as a part of the vegetable growth is^ of course, very 
smalL The water simply serves to convey the soluble foods of th^ 
soil to the various fibres of tlie plant. The actual amount of 
water used in irrigation is not a fair criterion of the amount 
needed for the development of plant life as in most cases crop^ 
arc over-irrigated. The actual depth and the rainfall and irri- 
gation water used on crops vary from as low as 12 inches ia 
sometimes as high as 16 feet, frequently running into quantities 




J 



Effects of Vegetation. 



135 



luch in excess of any ordinary rainfall in moist climates where 
f irrigation is found to be unnecessary, 

In the Report of the Kansas State Board of Agriculture for De- 
cember 51, 18S9, Mn W. Tvveeddale, C E., gives the following ta* 
ble containing the results of investigations by M, E- Risler, a Swiss 
observer, upon the daily consumption of water by different kinds 
of crops : 

TABLE, X 
Daily Coftnumption of Water hp CrfipB, 



Crops. 



Lucem grass, . 
Me^idQW grass* 

Oats 

Xndiaa Coin . . 
Clover* ....... 

Vineyard 

Wb^b ..**... 

Rye... 

Potatoes, ,.*. . 

Uak trees 

Fir Trees . , . . 



Ikches or Watxe, 



Minimmij, Maximum. 



0/J34 


0.267 


0,122 


0.287 


0J4il 


0.103 


o.no 


1,570 


0.140 




0.03,5 


0.031 


0-106 


0,110 


0,091 




0.038 


0.055 


0.03LJ 


0,038 


0.()2i) 


0.04S 



Mr. Tweeddale finds that this table agrees with careful experi- 
ments made in France and elsewhere, and calculates from it that 
from seed time to harvest cereals will take up 15 inches of water 
and grass may absorb as much as 37 inches. 

This table shows also one of the important reasons why a de- 
crease of stream flow follows the destruction of forests and their 
replacement by meadows and cultivated fields. It is quite evident 
also that if the watersheds were covered by grasses or cereals there 
would be comparatively little water left for the flow of streams. 
From this it will be seen that the character of the vegetation on a 
watershed exerts a considerable influence on the ultimate distribu- 
tion of the rainfall. 

The presence or absence of forests has also, as shown by a series 
of observations in Germany, a marked effect on evaporation. Prof, 
M, W- Harrington (see Bulletin No* 7, U, S. Dept. of Agriculture, 
p, 97) has compiled the accompanying diagram (Fig. 68), w^hich 
illustrates clearly the effect of forests upon the monthly evapora- 
tion- The upper curve represents the evaporation from water sur- 



136 



Disposal of the RainfalL 



faces in the open country, while the lower ctirve shows the evap- 
oration from water surfaces in the woods. The shaded area thus 
lUust rates the saving due to the cover and protection of forests. 

83, Percolation, — On pervious and unsaturated strata a portion 
of the rainfall sinks below the surface until it reaches a saturated 



4 




Fig. es.— Reduction in ESvaporatlon Due U> tlie Presence or Forests. 



or a relatively impervious stratum. The water then follows the 
of the stratum until it reaches an outlet along some stream or 
pears in the form of springs, frequently in an entirely dtflFerent' 
drainage area or possibly below the level of the sea itself. It is 
this ground water that gives rise to the dry weather flow of 
streams, and frequently is the only source from which stream flow 
is maintained during the dry seasons of the year. The same sources 
frequently maintain the winter flow at times when the rainfall is 
stored on the watershed in the form of snow and ice. 

Percolation is an important factor in the storage of water and 
in the construction of raceways and canals and needs most careful 
attention when such works are under contemplation. 

A large amount of valuable data concerning the losses due both 
to evaporation and seepage has been collected by Mr, E. Kuichling 
in connection with the study of the water supply for the New 
York Barge Canal and is reproduced in the Appendix. 

A small portion of the ground water is taken up by the roots <dU 
plants and frequently feeds vegetation during dry periods. Water 
drawn from the soil for such purposes, after fulfilling its functions 
in vegetation, is transpired from the vegetable surfaces into the 
atmosphere. Streams fed from areas where large deposits of fine 
grained but porous material are developed, are usually more 
constant in flow and less subject to fluctuations either from 
flood or drought. The flows of the deeper strata usually pass far 
from the watershed on which the rainfall occurs and modify to a 
limited extent the stream flow in other valleys frequently far from 
the original rainfall source. 



Evaporation. 137 

S4. Evaporation. — Evaporation takes place from moist surfaces 
and from the water surfaces of swamps, lakes, streams and the 
oceans, whenever such surfaces are in contact with unsaturated 
atmosphere. The absorption of the rainfall by the strata effectively 
limits the amount of evaporation from a given area by reducing 
the area of contact of wet surface with the atmosphere, thus con- 
fining the evaporation largely to free water surfaces. Fig. 69 
shows a map of the approximate annual evaporation which takes 
place from water surfaces at various points within the United 
States. It will be noted that this map shows, in the greater por- 
tion of the United States, evaporations equal to or greater than 
the annual rainfall at such localities. The total annual evaporation, 
IS shown in the map, is based, however, on free water surfaces 
only, and evaporation from ground surfaces only takes place from 
xcasional moist surfaces which occur after rains and when the 
humidity is high. The total amount of water evaporated, there- 
fore, is very much less than that which the map would seem to in- 
dicate This map and the table of monthly evaporation in the 
appendix are taken from data given in the Monthly Weather 
Review of September, 1888. The Weather Review observations 
are not based on absolute evaporation tests but are deduced from 
readings of dry and wet bulb thermometers as observed at various 
Signal Service Stations in 1887 and 1888. These deductions are 
supplemented by observations at several stations by means of the 
Piche evaprometer. While evaporation, like rainfall, varies from 
year to year in accordance with the variation in the controlling 
factors, yet in lieu of more extended observations this map and 
table indicate relative conditions at the various stations and ap- 
proximately the evaporation from free water surfaces. The com- 
parative monthly evaporation at sixteen stations distributed 
throughout the United States is shown graphically by Fig. 70. At a 
number of Eastern points, namely, Boston, Rochester and Nevi 
York, evaporation observations have been made for a number oJ 
years and from the data thus collected a knowledge of the local 
variations that cxrcur in evaporation at these points can be obtained 
Evaporation is greatly promoted by atmospheric currents which 
nave perhaps the most marked effect of any single influence. The 
temperature of the water and the humidity of the atmosphere also 
"^^c a marked effect. Mr. Desmond Fitzgerald in a paper on 
^^poration (see Trans. Am. Soc. C. E., Vol. XV, page 581) offers 
*"« following formula for evaporation : 



ifg* itr i-atf* igy_ itr_„ itr nr lu- ny nr ipg* Jpt* 




sr ftSf* ir ar ta^ «• «^ rf* rs* nr rr tr ir «F 


1 

»• 


M4rAyt'1^^^^ \M 






? I _—J-isiriv^ 1 \ \\rj^ \ X^'-^j^-^ i" t2vO\>C/ 


45" 


;;HrT^ \v^^ 




r>t>nS^i''H* ^ h v.L--'^*^^ \ \ JV>. if?.-^^ \ k 






;:=$rT5,, . VV'T^ 


S^ViWl'iK \] 


4** 


^^EaAj 


^!.^i^ 


JW— T^ 


^ 




&V- 


4V 




^NdLW-MJT^^^^i^^^r^^S^ *\ 




W V ■ - Tf*! J 


i^SeM13J 


ir 


fe^^J^li.^^'^^^-feL^S^^ \ \ 






IT 


1 f 23.---I ^.V7fs^^*«fYV* '' Wfc^t^ L---'---^''^ \ 




f H\A^X^ £-^^k\''\ \ 






»r 






ir 






tut 


;i S r ^ H-fS^*' V i i^V^^ri \ 




V / t n^S?L y 1 - hI ^1 L— -4 




jL \/ ^\ \ \\M/ A:£^-^-^c^ r 




K\ Ift -+4-^4R^T>r'*^^ HI "^^ 1 \ ANNUAL 


tr 1 


l^^^^qT^^ U— 4""'^^*? W ^''^' *'''^^- STATE S 






^ 5 ;^4iC-iJ^ 1 1 ll^?^ ^ ]J^ ^ a »,^r„„ ,(„«.,»„.(» 


ET 


^ 


L4Llli--^-IIP 


'Y'^ 








L-i-4-4-T 


\ tv^^,— T— ^ \ 


If 


"ia* -w- t*' tl* aft* 13* 81* 70^" Tf* "IP f 


^_ 


, 


1^ 


1 



140 



Dispo£ial of the RaiDtall. 



Sr 



m^ 






mMmmmmmmmmmMmMmMumi 



M. 



No. AtlAntf«> 

Hew HftTtifi, C'OQO, 



So. AtTantlc* 



St. LftWT^POP, 
DeuoLt, MIcIl 







HoDteOHiery, Ala. ral^tlns, Tex. 



Upper Ml^sIsflSppU Low^r Mtwla»lpp!g 
Dq» Moiae^ la, LitUe R<>ck, Ark. 






o 

R 

&4 




I 



Tt>p«k^. KAflS. Helena, Monc 



Red iJiviTt Ko. rttc<!i<.\ 

Hoorehead, Minn Olympic, Waitu 




Co1urnhl&, nKriAfl^ Colorado, 

Spokane, Wanh. f>ft<:ram«ikto, Oal, Yunm. ^rli. 



©feat 1 
Wi tine mil cca, H*v. 



Fig, 



lii.— Monthly Evaporation From Free Water Surfaces at Various Potnbi 

in the Untted States. 



I 



k. 



i 



I 



Evaporation. Z41 

E= (V-v)C+^) 
60 

In this formula V equals the maximum force of vapor in inches 
of mercury corresponding to the temperature of the water; v, the 
force of the vapor present in the air; W, velocity of the wind in 
miles per hour; and E the evaporation in inches of depth per hour. 
The value of v depends on certain relations between the tempera- 
ture of the air and the water. From a careful examination of the 
formula it will be seen that evaporation as represented thereby does 
not depend largely on temperature. 

Table XI is taken from a paper on "Rainfall, Flow of Stream, and 
Storage" by Mr. Desmond Fitzgerald (Trans. Am. Soc. C. E., Vol. 
XXVII, No. 3), and shows the monthly evaporation from water 
surface at Boston, Massachusetts, for sixteen years. The table is 
partially made up from a diagram of mean monthly evaporation but 
only when the observation practically agreed with the same. 

85. Evaporation Relations. — Professor Cleveland Abbe gives the 
following relations of evaporation, as established by Professor 
Thomas Tate : 

(a) Other things being the same, the rate of evaporation is 
nearly proportional to the difference of the temperature indicated 
^y the wet-bulb and dry-bulb thermometers. 

(b) Other things being the same, the augmentation of evapora- 
tion due to air in motion is nearly proportional to the velocity of 
the wind. 

(c) Other things being the same, the evaporation is nearly in- 
versely proportional to the pressure of the atmosphere. 

(d) The rate of evaporation of moisture from damp, porous sub- 
stances of the same material is proportional to the extent of the 
surface presented to the air, without regard to the relative thickness 
<5^ the substances." 

(0 The rate of evaporation from different substances mainly 
depends upon the roughness of, or inequalities on, their surfaces, 
the evaporation going on most rapidly from the roughest or. most 
uneven surfaces ; in fact, the best radiators are the best evaporizers 
^^ nioisture. 

(0 The evaporation from equal surfaces composed of the same 
material is the same, or very nearly the same, in a quiescent at- 
"'osphere, whatever may be the inclination of the surfaces ; thus a 



143 



Disposal of the Rainfall. 



I! 

I 

I 



< 



to 



I 



C3 

I 



8 



S 



's 



p 









II » * 















o I- Om -f io ^ S c^ ^ s^ iQ 






* * * # ♦ * 



■^^ kO O 30 'S* -^ -*■ W 71" OQ 05 ^ 

Cv c: i>» o -H c^ o ?5 o lO C4 ^n 






o o i-* oi *r ■+ tO M -**• ^ ^5 lo 









s 



s 



s 



§ 



s 



fet: 5 



■3 



a 
M 

I 









I. 



Evaporative Relations. 



14? 



horizontal plate with its damp face upward evaporates as much as 
one with its damp face downward* 

(g) The rate of evaporation from a damp surface (namely, a 
horizontal surface facing upward) is very much affected by the 
elevation at which the surface is placed above the ground- 

(h) The rate of evaporation is affected by the radiation of sur- 
rounding bodies. 

(i) The diffusion of vapor from a damp surface through a 
variable column of air varies (approximately) in the inverse ratio 
of the depth of the column, the temperature being constant, 

(j) The amount of vapor diffused varies directly as the tension 
of the vapor at a given tempera tare, and inversely as the depth of 
the column of air through which the vapor has to pass* 

(k) The time in which a given volume of dry air becomes satu- 
rated with vapor, or sattirated within a given percentage, is nearly 
independent of the temperature if the source of vapor is constant. 

(i) The times in which different volumes of dry air becone 
saturated with watery vapor, or sattirated within a given per cent^ 
are nearly proportional to the volumes. 

(m) The vapor already formed diffuses itself in the atmosphere 
much more rapidly than it is formed from the surface of the water. 
(This assumes, of course, that there are no convection currents of 
air to affect the evaporation or the diffusion,) 

86. Practical Consideration of Losses. — From the previous dis- 
cussion it will be readily realized that it wOuld be impossible to dif* 
ferentiate all of the methods of the disposal of rainfall upon a drain- 
age area. Evaporation differs widely from different classes of vege- 
tation and from different classes of land surfaces; also on account 
of the slope and exposure. No two square miles upon a drainage 
area offer the same conditions as affecting evaporation which differs 
very widely with such conditions. Evaporation and seepage from 
any surface varies with the temperature, with the moisture in the 
air, and with the \^elocity of the wind. Tt is therefore impossible 
to compute, with any degree of accuracy, evaporation over an ex- 
tended surface of a watershed or drainage area, or to ascertain 
with any degree of accuracy the probable losses that will take place 
in the same area. 

For water power purposes, the rainfall can, therefore, be divided 
into two quantities in which the water power engineer is interested: 
First : The run-off on which the power developed directly depends. 





144 



Disposal of the RainfalL 



and, Second : The losses, by whatever means they occur, which are 
not available for such purposes* Evaporation is usually but not 
always the source of greatest loss on a drainage area and commonly 
other sources of loss are insignificant when compared with it It is 
therefore a common practice to deduct the run-off from the rainfall 
on a given drainage area and to classify the difference as evapora- 
tion, including under this term all losses of this same general 
character, whether through seepage, evaporation or otherwise. _ 



LITERATURE. 

1. Vtrmeule, C, C. Report on Water Supply. G€oL Sunrey of New Jener^ 

Vol. IIL 1S94. 

2. Yermeule, G. C. Report on Forests. Geol, Surrey of New Jersey, 1S99. 

3. Turneaur© and Rusaell, Public Water StippUes, Chap* V, New Yorfe, 

Wiley & Sons, 1901, 
4* Rafter, George. Hydrology of tlie State of New York, pp. 46-197, Al- 
bany, R Y. New York State Education DepL Bui. SB, 1905. 



FEECOLATIOK. 






5< Law€S, J, B, The amount and Composition of the Rain and Draia 

Waters Collected at RoUiamsted. Jour, Royal Agrlc. Soc 

England, Vol. 17; p, 241, 1881; Vol, IS, p. 1, 1882. 
€. Fortier, Samuel, Preliminary Report on Seepage Water, and The Un^ 

derflow of Rivers. Bulletin No. 38, Agric Bxpt Statlos, Lops. 

Utah, 1895. 
7, Seepage or Return Waters from Irrigation, Bulletin Na S3. Colo* 

Agrlc Expt Sta., Fort Collins. Colorado. 1896, 
S. Fortler, Samuel. Seepage Water of Northern Utah. Water Supply as A 

Irrigation Paper No, ?, 1S97* 
9. The Lost of Water from Eeservoirg by Seepage and Evaporation. Bill' 

letin No. 45, Colo, Agrlc. ESxpt Sta., Fort ColUns, Colorado. 

May, 1898, 
10. Loss from Canals from Filtration or Seepage. Bulletin No. 4S. Colo. 

Agric, Expt Sta., Fort CoIUhb, Colorado, 1898. 
11* Kulcbllng, EmlL Loss of Water from Various Canals by Seepage. (See 

paper on Water Supply for New York State CaaaJSp Report of 

State Engineer oa Barge Canal, 1901). 

12. Wilson, H, M. Irrigation Engineering. New York, Wiley 4 Sons. 1901 

13. Wilson, H- M, Irrigation In India, Water Supply and trrigallon Paper 

No. 87. 1903. 

14. Mead, D. W, Report on Water Power of the Rock River, Chicmgo. Pub. 

by the author. 1904. 



15. GreaTei^ Charles. 
1875-76. 



ETAPORATIOIC^ 

Oa Evaporation and on Percolation. 

Vol. 46, p. 13. 



Proc Inst 



Literature. 145 

16. Fitzgerald, Desmond. Evaporation. Trans. Am. Soc. C. E., Vol. 15, p. 

581. Sept» 1886. 

17. Loss of Water from Reservoini by Seepage and Evaporation, BuUetin 

No. 45, Colo. Agric. Bxpt Sta., Fort Collins, Colo. May, 1898. 

18. Depth of £?vaporation in the United States. Monthly Weather Review. 

September, 1888. 

19. Depth of Evaporation in the United States, Engineering News, Decem- 

ber 30th, 1888; January 5th, 1889. 

20. Harrison, J. T. On the Subterranean Water in the Chalk Formation of 

the Upper Thames and its Relation to the Supply of London. 
Proc. Inst C. E. 1890-91. Vol. 105, p. 2. 

2L Femow, B. B. Relation of Evaporation to Forests. Bulletin No. 7, For- 
estry Div., U. S. Dept A2Tic and Engineering News, 1893, Vol. 
80, p. 239. 

21 Kimball, H. H. ESvaporation Observations in the United States. Read 
b^ore the Twelfth National Irrigation Congress, 1904; E«ngi- 
neering News, April 6, 1905. 

USB OF WATVB IN AGBICULTUBK. 

The Publicatioiui of the United States Experiment Stations on Irriga- 
tion and of the Experiment Stations of the various States contain much 
information on this subject The following are of especial importance: 
:i Hill, W. H. Report of State EAagineer to Legislature of California. 2 
Vols. Sacramento, 1880. 

24. Carpenter, L. G. Duty of Water. Bui. 22, Agric. Elxpt Sta., Fort Col- 

lins, Colorado. 1893. 

25. Fortier, Samuel. Water for Irrigation. Bui. 26, Utah Agric. Expt Sta., 

Logan, Utah. 1893. 

20. Report of Irrigation Investigations, U. S. Dept Agriculture, Irrigation 
Inquiry. Bui. 86 for the year 1899. 

27. King, F. H. Irrigation and Drainage. New York. MacMillan Co., 1902. 
The amount of Water Used by Plants, pp. 16-46. Duty of Water, 
pp. 196-221. 
2S Head, Elwood. Irrigation Institutions, Chap. VII, The Duty of Water. 

New York. MacMillan Co. 1903. 
29. Wilson, H. M. Irrigation Engineering, Chap. V., Quantity of Water Re- 
quired. New York. Wiley k Sons. 1903. 



CHAPTER VIIL 



RUN-OFF, 

87. Run-Off, — That portion of the rainfall that is not absorbed 
by the strata, utilized by vegetation or lost by evaporation, finds 
its way into streams as surface flow or run-off. The demands of 
the first named factors are always first supplied and the run-off is 
therefore the overflow or excess not needed to supply the other 
demands on the rainfalL The run-off, therefore, while a direct func- 
tion of the rainfall, is not found to increase in direct proportioTi 
thereto, except perhaps in seasons such as early spring when from 
seasonal conditions the demands of vegetation, percolation and 
evaporation are not active and all or most all of the rainfall flows 
away on the surface. The remainder of the year the run-off may 
be said to increase with the rainfall but usually at a much less 
rapid rate and in many cases the rainfall is entirely absorbed by 
the strata or vegetation, and does not influence or affect the run-off. 
In this case the run-off is supplied from the ground water, stored 
from previous rainfalls, and is entirely or largely independent of 
the immediate rainfall conditions. 

An examination of the observed run-off of streams, and the rain- 
fall on their respective drainage areas, for annual, monthly and sea- 
sonal periods, will show that there is a relation more or less direct 
between the rainfall and run-off (see Fig, 71, ct seq,). The relations 
are shown by various diagrams and mean curves from which many 
departures will be noted. The departure of individual observations 
from the mean curve expressing these relations shows the relative 
importance and influence of other factors in affecting such relations- 
The relations of the numerous factors which are known to influence 
the results are quite complex and are not well established and mudt 
more meteorological information in much greater detail and a care- 
ful consideration and study of the same will be necessary bcforfl 
such relations can be even approximately established. 






^ io •« <v» eq 




143 



Run-Off- 



88* Influence of Various Factors, — Tlie influence of various 
factors of disposal was discussed in the last chapter. Evaporatioo 
is known to vary with temperaturCj the direction and velocity of 
the winds, barometric pressure, and various other meteorological 
influences, and yet no clearly defined relation has yet been shown 
to exist between these factors, by means of which their actual in- 
fluence on the run-off can be approximately calculated. Mr. C C 
Vermeulc (see Vol, III, GeoL Survey of New Jersey) considers 
that annual evaporation depends largely on the mean annual tem- 
perature and offers a formula for the calculation of the same^ which, 
in many cases, gives results which seem to agree closely with the 
facts and data collected from a number of Eastern drainage areas. 
Mr. Vermeule s formula for the relation between annual evaporation 
and precipitation on the Passaic River, and some other Eastern 
drainage areas where conditions are simitar, is; 

£^15,50+0.16 R 
in which 

E^The annual evaporation (including all lasses on drainage ana 
except from run -off) 

and R^the annual rainfalL 

For general application to all streams he suggests the formula 

E=(i5.5o-|-o,i6 R) (0.05 T— 148) 

in which T^ mean annual temperature. 

Mr, Vermetite also offers a formula for the evaporation for each 
month and discusses at length the influence of ground storage on 
the flow of streams* Mr, Geo, W. Rafter (see Water Supply and 
Irrigation Paper No. 80) has made a careful analysis of available 
data which indicates that no such intimate relation can be found to 
exist. In general, the information available does not seem to show 
that other factors have a sufficiently definite relation to nin-off ofj 
to each other to make such relation clearly manifest and y^t such 
factors are known to have an unmistakable and constant influence, 
This fact is quite clearly demonstrated by a number of diagrams 
prepared by Mr. Rafter, which are here reproduced. 

Figure 72 shows graphically the relation between precipitation^ 
evaporation, run-off and temperature on the Lake Cochituatc basin 
for thirty- three years. In this diagram the years are arranged !« 
accordance with the precipitation. In a general way the evapora- 
tion and run-oflF for these years may be said to vary with the pre- 



1 




flucnce 



K::i:;:»:;ii;::::;HH:: 



!s::::::::i::::::::;:::: 




JH 

Xi 

a 



iai ii ii i i i iiiiiii ii ■ i 

■* ■■«■■■ ■•■■»■■■■ r- ■■ 
■■'■'■««■■■■■■>■■*«■■■■ 
■■ ■! ■.«■■ ■■■■■>■■■ ■■'«'« 







iill 


!■■■ 


ill 


■ ■■1 






zz 


l.iiiiH = 


^■■■fl 








■■■■■I 


■ ■■ 


::" 


«« 


k«i 


■■■1 


::::: 




:s 




sssss 



k 



!»:»»: ::!sb»::s:8:::8:»h::»: 



H 


■■■• 

::: 

■■■ 

[»: 

■ ■■i,q 

■ ■■fl 


KtP 


■ ■■ 

ills 


PIT' 

4?^ 


w 

:: 

il 

■ ■ 1 

■ ■ 1 
«■' 1 
■• 1 






h:::;:::;;::!:;: 



::»;;: :::i::i:::!':: 






?i itniiiiiiit lUHiiiii ••■■•••••I 



»::»8lM«s:::::»H»:: 



-ii!! !!!! if !■!!!- 



iiiiiiiiiiiiiiiiiiii 



■ ■• ■ ■!■!■!!•■ !!!!!li»li ! 



Years arranged in order of dryness, 

FIf. 7S.^RelatIon Between Precipitation. Eiraporatlon, Run-off and Temperir 
ture oa Lake Cochituate Basin. 






ISO 



Run-Off, 



cipitation. Evaporation, wliicb, it must be remembered, here itP 
tludes all losses except that due to run-off, increases in g^neraJ 
as the rainfall on the area increases and decreases with the rainfall. 
For limited periods, however, this general law does not hold. 
Other factors affect the relatiuus and cause material departures 
from the general law. This is particularly marked in the years 1891 
and 1872. For these two years The rainfall was almost identical in 
nmount- The evaporation for \he same years, however, differed 
materially, being about 16 in*^hes less in Wji than in 1S72* As 
a consequence the run-ofl lo^ the year 1891 was about l$% inches 
greater than in 187;^. 

In order to demonstrate the mutual relation between evaporation 
tnd temperature the d^ta illustrated in the previous figure has been 






SO 



^0 - 



^: 



3^ 



2Q 



to 



HM^^iMt 



¥fan 



t On Us ta ^ • 



10 to^^q%C«^«w*«<-«»|ii»>AOitoe4»iiSr4Yn> 



Wig, 73.— Relatfon Ectweea Evaporation auo Temperature on Lake Cocbltust* 

Basin. 

Years being arranged according to amount of eyaporatlon. 



k 



Influence of Various Factors* 



151 




Fipf. 74,— Relations between Preelpl- 
Nation, Run-0£f, Evaporadon and 
Temperaturtj on Sudbury Hifcr 
Biain. 

Yean arranged acscording^ lo regnlar 
orcleFi dryne^JB and de^rea^iiig evapo* 
ration regpDCU?elyt 



i 



jtr ur K5* nsr nr tir nr m* nr ui' nar tor 




ps^^ 






^ 



15+ 



Run-Oi* 



«0 



so 



40 



00 



20 



ro 




44^ 
%4^ 

S4€f^ 



10 



jia 



'» 



ttt^tt 




to 



s& 



' ■ H-i-HH+1 rH 










^ -^ ■ _ I 






g - - ■ 






























4#** — -» _ _- 




= — ^^ , ~ ^_-i_^ 








^ _ 


42<s ___^=_;__II 






4^0 r_- 






40O —^ ^^- 


;jpo 


IIIIIIIIIIH 



rta^lllllillllllll 



r£>uia||§sl3i§rE2 



Pig. 75.— Relations Between Predpttation, Rtin^ff. EvaporaUon and Tempertr 

ture on Upper Hudson River. 

Years arranged according to regular order and decreasing etaporatloa, 

rearranged by Mr, Rafter, and in Fig^ure 73 the relation for the 
years has been arranged in the order of their evaporation, and com- 
pared with the mean temperature for the year. This figtire serves 
to show that while temperature may, and unquestionably does, 
influence evaporation, yet the mean annual temperature has no 
controlling effect on the annual evaporation. It will be noted that 
for the year 1878, when the mean temperature was a maximum, the 
evaporation was considerably below the average for this drainafT 



^ 




Relations of Annual Rainfall and Run-Off. 



155 



area. Similar relations for the Sudbury River basin are shown in 
Fig. 74 and for the Upper Hudson River basin in Fig. 75. 

89. Relations of Annual Rainfall and Run-Off. — Figure 76 is a 
mean run-off map of the United States and should be compared 
with the map of average rainfall. The run-off as shown by this map 
is expressed in inches on the drainage area and similarly to the com- 
mon expression for the amount of rainfall. The value of this map 
is comparative only. In this case, as in the cases of rainfall and 
evaporation, the mean conditions are subject to wide variations. 
A detailed study of local conditions is always necessary in order 
to fully understand and appreciate the influence of extreme condi- 
tions and of local factors. 

The relation between the annual rainfall and run-off on various 
drainage areas is shown in Figures 71 to 75, inclusive, as previously 
described. The mean relations between these two factors on four 
selected drainage areas are, however, more clearly shown by the 
graphical diagrams Figs, yjy 78 and 79. From these diagrams a 




Fig. 77. 




Pig. 78. 



ISO 



RuD-Qfi. 



fiieaa relation can be traced for each area from «inc3u bcnrem, 
tlsere are considtnblt depaniires in indrridial jcns. Tbe saidj, 
therefore^ of this subject on this basis will deiDonssxxlc l3ie aen 
relation and tbe departure therefrom which imisr be rij>r» ird <■ 
the area considered and other areas where physical ciwfilimis aic 
similar. 



* *y^_ M<* A** X" AM *• «fll tf^ tt »» 

I 



1 1 r-r-r-T L4-]- 



Fig. 79 



Table XTl.^Mu$kingum River, 1888-1S95, inrluftire, 
(Oifchnwnt mn^^^bjn aqnaxm mOm§,1 







]M. 


1 


1889. 




MIL 


Period. 


Rain. 


Kan- 
off. 

5.17 
1.77 
3.39 


Erspo'i Bahi- 
ntioni IftlL 


Rob. 
off. 


Etbpo- 

ntioB. 


5£" 


^ 


ss 




iT.ie 

14.31 
11.14 


11.99 
12.64 
7.75 


13. « 
12.12 
10.24 


6.02 

.96 


7.80 
10.88 
8.28 


xr.n 

13L88 
15.91 


M.flr 

8.81 
8LI8 


9L« 


Orowlnif 


ILN 


BtpleniMhlnff 


9lS 






Y«*r ...«. 


42.01 


10.33 


32.28 86.88 


8.22 


27.66 


S8.tr 


88.81 


880 










im. 




18tt. 


1898L 


Storain* 


16. T8 
13.80 
7.08 


12.42 
1.77 
1.87 


4.30 
11.79 
6.71 


20.39 
16.64 
4.81 


9.06 
8.65 
.67 


1L83 
18.89 
4.14 


25.04 
8.81 
ft. 01 


14.18 
LIS 

.86 


ma 


Growing ^ 

B«pl«niiihfn|f .............. 


7.» 






Year 


87.38 


16.60 


21.80 


41.74 


13.86 


28.86 


a.88 


ULSO 


811I 










1894. 




jtm. 




SiulUPO 


16.98 
4.56 
9.02 


T.63 
.66 
.41 


8.80 
&90 
8.61 


18.01 

" 8.U 

7.66 


4.04 
.49 
.87 


18.81 


OrowlofT .... ...................•.>«.•.••..•...••> 




Ntf 












y#ar 


80.61 


8.70 


n.oi 


89. 84 


,4.80 


tLtt 




Ji^ 



The Water Year. 157 

gK>. The Water Year. — ^The relation of annual rainfall and annual 
n-oflF is more or less obscured by variations in the periodic dis- 
bution of the annual rainfall. A study of the relation of the 
riodic rainfall and the periodic run-off is therefore necessary. 
For a comprehensive understanding of the relation of rainfall to 
in-off it is more convenient to refer to the water year instead of 
le calendar year. The water year is the annual division of time 
lat represents the full annual cycle of change in hydrological 
)nditions. It does not, as a rule, conform very closely to the calen- 
ar year, neither is the water year constant for each annual period 
I its beginning or end, but varies as meteorological conditions 
ary. 

As previously stated, in the greater portion of the United States, 
he water year naturally divides itself into periods, beginning, ap- 
proximately, with December, and ending, approximately, with the 
oUowing November. The period from December to and including 
Way is termed the "Storage" period ; June, July and August con- 
Jtitute the "Growing" period, and September, October and Novem- 
ber are termed the "Replenishing" period. Not only the year but 
Jiese periods as well vary each year, and are not necessarily 
limited by our artificial division of calendar months and years. 

During the storage period, the snows of winter and the rains of 
spring saturate the ground, and a large amount of water is held in 
storage in lakes, swamps, and forests, and in pervious soils, sands 
and gravels. The portions of this stored water tributary to a drain- 
age area but not necessarily within the boundaries thereof, and at 
elevations above the level of the stream, are, when conditions de- 
mand, available to supply the stream flow, and are also available 
for the purpose of sustaining plant life. Such waters will feed a 
stream to an extent depending on their character and magnitude, 
regardless of the amount of the immediate rainfall, and will cause a 
stream to flow for several months, even without rain, if the per- 
vious deposits and other storage resources are well developed 
upon the area. These relations vary widtly with each individual 
area, and in areas not well provided with such deposits the streams 
^ften run dry through the warm days of summer. 

Whenever the surface of the stream falls below the ground water 
gradient the ground water is affected and begins to supply the 
»tream flow. This sometimes occurs early in May, and seldom 
ater than the beginning of June. During June, July and August 
he rainfall is rarely sufficient to take care of the evaporation and 



15S 



Run-Off, 



growth of vegetation without something of a draft on tl 
water, and the stream flow during this period is usually entirely 
dependent on the ground water, except during exceptionaUy heavy 
rainstorms. By the end of the growing period about August 31st 
the ground water is often so reduced as to be capable of storing 
several inches of rainfall. During the replenishing and storage 
periods of winter and spring the ground begins to receive its store 
of water, and. with favorable rainfalls^ the ground becomes fully 
saturated by the end of April or May. 



Table Xlll.—Hudmn Himr^ 1S8S^1901, inctimve. 



^ 





lase. 


ll». 


wm. 


F^rbd. 


Batxi- 


Bim* 




Ratn- 
fmlL 


Run* 


Ktupcv 


Rahi> 

tea 


Bun- 
oil. 


twtw^ 


ORnHnt. >,,...». 




IT.OA 
1.CG 


19* 

a. SO 

9.H 


ILIO 
15.05 
10,81 


ILOt 
4.SS 

an 


aoft 

10. 7B 
r.40 


£4.15 

U.10 


1Sl» 
2. IS 

CBl 


lOffi 


Tbwf »„««,-—<... 


4a«i 


1^.04 


».» 


«ie.9e 


Ei.n 


£!.» 


(!fio,afr 


BS.M 


tift 




1ML 


leiOL 




upa 




Steimff* ,_.>.,.^-,..w._. 


SO. OB 

laid 


L9Q 


i.10 

ll,it 

e,i8 


i4.a& 

lV.lt 

f.ao 


an- 


aia 


ia«a 
lajfT 
a 98 


i&ao 
fiii 
an 


4.9 




1£L9 


B^|ft^tll)lllAg i,m,,m,, .....> 


IK 






Tau... _. 


4^m 


soice 


mm 


mer 


sa 08 


fD.T^ 


4£.ia 


ti.fiii 


m.n 




3JM. 


18»v 


urn. 




Btenffs ._. 


n.8T 


lais 


a. It 


1&.7V 

msr 

10. » 


a«s 


4.11 

a 01 

T.O0 


ttii 

IDES 
12,7? 


laa 
ass 

4.08 


aa 

T It 


Seple^iJfiliiQjf ,.^.^»«..:....^ 


an 


Yaw..... ._.,-.. 


IL07 


IS. ST 


^.eo 


W.S7 


IT. 4ft 


IS. SI 


iSvH 


latt 


21. W 




imft 


mei 


i»a 


matmg9 .„. 


19.77 
10. M 


14.60 
f.7» 

aao 


6. IT 
8.01 
T.14 


2&80 

12, li 


laa 


4.11 

mfs 
a«e 


12.48 
7.40 

aai 


i«.ifi 
lis 


aiT 
an 






Tmr ................. 


U.ffI 


»L1« 


SO.tt 


4A.bi 


n.iiB 


si.w 


K.79 


IfiiH 


las 














liOO. 




UDU 






.™„. 






£1.1S 

i».'n 
i£.n 


18.11 

aso 
a» 


lil. 
0.1S 




It. SI 

its 

a 


Ett 

llff 




att 












Year...... 


Ilk 11 


ftX«f 


14.74 


u,m 


11. tt 


mn 





i 



' .A.fiproxXaiit& 




Relations of Periodic Rainfall to Run-Off. 
Table Xiy.—ConnectictU River, 187S-1886, inclusive. 



IS9 















187& 


1878.- 


1874.a 


Period. 


Ralxi- 
telL 


Ron-- 
off. 


Erapo- 
ration. 


Bain- 
fall. 


Run- 
faU. 


ETapo- 
ratioii. 


Bain- 
faU. 


Ron. 
off. 


ETapo-^ 
ration. 


fitorsffd 


14.98 
18.96 
lS.tf 


1&80 
6.S8 
6.64 


1.68 
12.67 
8.78 


18.16 
10.11 
U.04 


21.80 

an 

5.28 


a64 
7.40 
a88 


sacs 

14.87 
7.76 


aaoi 
a68' 
ai5 


aoi 


Orowioff ....... .........r-« 


7.m 




a61 


Ymr 


48.80 


8B.8S 


2a07 


4a 81 


88.78 


ia66 


45.21 


8L81 


ia40 


Pvriod 


U75. 






1876.0 




i8n.; 


Stonoe 


17. n 
14. » 
11.85 


8.80 
8.60 


8.01 

io.:5 

7.76 


28.60 

lau 
law 


24.74 

asft 

a28 


( 

-a24 

0.16 

a 89 


laoo 

14.00 

iao8 


laoB 
aoi 

6.87 


a4i 


Orowinc .....,..' 


11.0» 
• 7.81 






Year 


4a 42 


88.87 


80. 6S 


46.66 


80.87 


16.81 


4aK 


8a 86 


84.81 






Pvrioo. 




Mm 


1878. 






i8sa 




8tof«»« i 


tl.88 

laao 

10.56 


18.tt 
8.4ft 

ao6 


a86 
10.14 
7.60 


28.19 
16.07 
9.48 


21.40 
a 02 

a 08 


1.70 

iai5 
a 56 


ia» 

11.88 
11.66 


14.78 

a46 
aos 


a6i 


Qtowlnc 


O.ST 


Bvplenishinv .^ 


age 






Y«tr 


46.08 


24.68 


21.S0 


48.74 


27.84 


21.40 


41.60 


ia85 


21. 8i 






l>«iod. 


Uffl. 


1882. 


188a 




»or«ge 

ItoplOTitelring 


»L88 
U.80 
11. 8B 


ULOB 
S.98 
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4.81 
8.87 
7.90 


»ao.fio 

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»a80 


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a 17 


a86 
aio 

4. 88 


^laes 

Ma 80 

»a20 


a78 
a6i 

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4.1» 

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• 4.88 


Year 


4&51 


IS. 84 


tl.l7 


8a 46 


17.66 


80L79 


&66 


ia6i 


19.94 






P«rk>d. 




1884. 






188a 




Storace 


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12.14 
a 51 


20.20 
a 79 

a 61 


1.22 
a 86 

aoo 


ia66 

14. 8t 
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ia68 
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ai5 












Year 


42.07 


».60 


ia47 


45.16 


8a 44 


SaT8 







«2lot included in mean. 



^Ralnfkll compnted, approodnuite. 



91. Relation of Periodic Rainfall to Run-OfF. — For streams where 
the observations of flow have been made for a number of years, 
comparisons can readily be made of the relation of annual and 
periodic rainfall and run-off. Such investigations should be made 
by the water power engineer when considering a river relative to 
its availability for water power purposes. An analysis of such 
data for the Muskingum, Hudson, and Connecticut Rivers as made 
by Mr. Rafter, is shown in Tables XII, XIII and XIV (for ad- 



i6o 



Run-Off. 



ditional tabular data see Appendix) » Graphical representations of 
the periodic relations of the rainfall and run-off on the Upper 
Hudson River basin are shown in Fig. 80, and the same relations 
ior the Sudbury River basin are shown in Fig. 81, 




10 U 2Q 29: 

Preclfiit^tfon in McAfu 




IQ IS 20 

PffClpttatfon in Inciiti 



S0\ 



a: 



h \ \ \ \ I \ 


A/ff^ period ^ 




\VTV\V\ 






^=-----= 





10 is JO 

PrwcSoltatkkn tn tnchtt 



25 



Fig. 80.— Rainfall and Run-Off of Upper Hud eon River for Each Ptrlod df Ito^ 

Water Year. 

[l>Dni W, a uut L P&psr Na, m "Relatloii of Balarftll 10 Iliui4>ft' ] 





Relations of Periodic Rainfall and Run-0£E. 



i6z 




ts m 2$ 



Pnclptiatlon tit fadits 
to 15 20 25 SO 



26 

lo\ lOr^ 














C 


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10 ' ' ';5' ' ' 'id' ' ' '26' ' ' 

PnelpitatlontnlnQliu 
10 16 20 25 


50 




I g g 



^ 8l-7Rainfall and Run-Off of Sudbury River for Bach Period of Oie 

Water Year. 



IFivm W. a And I. P&per No. 80 *'ReIaUoii of B*infaU to RuB-Off.**] 



i62 Run-Oflt 

92. Monthly Relation of Rainfall and Run-OfF. — ^The relations of 
rainfall to run-off from month to month on a given drainage area 
are not usually as direct and definite as the annual and periodic re- 
lations. The mean and extreme relations can, however, often be 
established within somewhat wider limits, and such relations will 
permit of the formation of at least a general idea of the probable 
limits of the monthly run-off, under other rainfall conditions. The 
wide range of the possible error of such estimates will be shown 
by the divergence of independent observations from the normal. 
To establish accurately the maximum and minimum limits, it is 
probable that observations, at least as extended as those needed 
for accurate rainfall estimates, will be needed. 

The observed relations between the monthly rainfall and the 
monthly run-off in various drainage areas are shown by Figs. 82, 83, 
84 and 85. 

On Fig. 82 are shown the relations of monthly rainfall and run-oflf 
for several Northern river basins, and on Fig. 83 are shown the 
same relations for several Southern river basins. An examination 
of these diagrams will show the marked effect of seasonal tempera- 
tures and conditions upon the quantity of run-off. The high per- 
centage of run-off in the spring should be noted ; also how the per- 
centages of run-off in these rivers drop with the advance of the 
season and rise again in the fall. 

On Fig. 84 are given the monthly relations of rainfall and run-off • 
for thirty years on three small river basins in the immediate 
vicinity of Philadelphia. These drainage areas, being small, are 
more readily and directly affected by rainfall, hence the relations 
are much more marked and uniform than those that exist on larger 
rivers. The marked variation from normal due to the influence of 
other varying conditions on the drainage area, especially during the 
summer months, should be noted. 

Figure 85 shows a set of monthly diagrams prepared by Emil 
Kuichling, C. E., for his discussion of the relation of rainfall to 
run-off in certain rivers in the Eastern part of the United States. 

On these diagrams the figures not enclosed are numbers of ob- 
servations from drainage basins Nos. i to 8 inclusive, of the fol- 
lowing list. The figures enclosed in circles are the numbers of 
observations from drainage basins Nos. i to 28, inclusive. 



I 

o 

c 

3 
I 



o 





Relations of 


Monthly Rainfall and Run-OfiF. 














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Horizontal Ordinatee — Rainfall in Inches. 



^ Wisconsin River at Neoedah. 
D Chippewa River at Eau Claire. 
A Grand River at Grand Rapids. 



V Grand River at Lansing. 
X Thunder Bay River. 
* Rock River at Rock ton. 



Fig. 82. — ^Monthly Rainfall and Run-off — ^Northern Rivera. 



164 



Run-Off. 



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Horizoatal Ordinates— EainfaLl in Inchea. 

* Talladega Creek, Watenebed Area 156 Square Milea, 
VUpadacheo River, ** " 440 " 

• Alcovy Eiver '* " 228 ** ** 

Fig. fi^.^-Monthly Rainfall and Run-Off-— Southern Rivera. 




Relations of Monthly Rainfall and Run-Off- 



I6S 



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DECEMBER | 












































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2 3 4 5 G 7 Q 9 10 II 13 13 14 
RAINFALL IN INCHES 
OBSE RVAT IONS 

J(*TOHlCKQN CREEK 
A^NCSHAMINY 
^3~ OFCRIiiOMEN 



OI234&6789I0II rZI3l4 
RAINFALL IN INCHES 
WATERSHgp AREA 
102,2 SQUARE MILES 
la©, 3 
1C2,0 ■ * 



Ffg. 84* — Relation between Koinfal! and Run-Off un Tohickon^ Neshftminj, aod 
Perkiomea Creeks near PbilBdelphiaT PennHylv&nia. 




1 66 Run-Off. 



V 




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*»iqatii m qiaoH J»d flO^^^H P H'^^^d a«*K 



J 



Relation of Monthly Rainfall and Run-Off. 167 

Watersheds from which Observations were platted on Diagram 86, 



No. 



Name of Basin. 



Area in Sq. 

Miles. 


No. of 

Years 

Reoard. 


338.0 


80 


152.0 


13 


139.3 


13 


102.2 


14 


75.2 


25 


43.1 


12 


27.7 


18 


19.0 


83 


40.0 


2 


51.6 


2 


69.0 


2 


63.0 




80.8 




104.0 




144.0 




153.0 




187.0 




191.0 




256.Q 
618.0 




2 


563.0 




822.0 


17 


879.0 




1070.0 




1306.0 




1889.0 




4600.0 


12 


5828.0 





1 

2 

3 

4 

6 

5 

7 

8 

9 



1 

2 

3 

4 

5 

6 

7 

18 

19 

20 

21 

22 

23 

24 

25 

26 

27 

28 



Croton River, N. Y 

Perkiomen Creek, Pa 

Neshaminy Creek, Pa 

Tohickon Creek, Pa 

Sudbary River, Mass 

HemJock Lake, N. Y 

Mystic Lake, Mass 

Cochitoate Lake, Mass 

Cayadutta Creek, N. Y 

Saquoit Creek, N. Y 

Oneida Creek, N. Y 

Nine-Mile Creek, N. Y 

Garoga Creek. N. Y 

E. Branch Fish Creek, N. Y 

Oriskany Creek, N. Y 

Mohawk River. N. Y., at Ridge Mills 

W.Branch Fish Creek, N. Y 

Salmon Ri ver, N. Y 

East Canada Creek , N* Y 

West Canada Creek, N. Y 

Schroon River, N. Y 

Passaic River, N. J 

Raritan River, N. J 

Genesee River, N. Y 

Mohawk River, N. Y., at Little Falls 

Black River, N.Y • 

Hudson River N. Y., at Mechanic ville, N. Y 
Muskingum River, Ohio 



A continuous graphical record for ten years, showing the rela- 
tions of rainfall to run-off on the Illinois River basin, based on ob- 
servations of stream flow made at Peoria, 111., is shown by Fig. 71. 

93* Maximum Stream Flow. — In the construction of spillways, 
dams, and reservoirs, and the study of their effect on the overflow 
of embankments, levees, and lands, the question of maximum run- 
off becomes important. 

Many formulas have been suggested by engineers for determin- 
ing flood flows, each of which is based on more or less extended 
observations, and are applicable only when used under conditions 
similar to those on which they are founded. Very few of these 
formulas take into account the great number of conditions that 
"modify the results. For this reason most of such formulas are of 
little use except for the purpose of rough approximation. None of 
these should be used without a knowledge of the conditions under 



i68 



Run-OfiE. 









* 

4 


1 ^ 

4 f 1 3 

5 i 1 S 'S 

■a 5 B |i . .y> S 

1 1 1 1 ^ 2 


i 


I . 


S - J _ 




1 1 -^ 

s :• 1 

+ + s 


««1 ! 

S « g 2 

1 ^ £ (S 

* ■- • 

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i.i_____L; 


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(S £ ' ' " 
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1 = li. = = 




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______ /JLIL 








7 H • • • 
















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i 
t 

s 

« 

9 

e 

s 

3 

r 









Max. rate oE Di^chat^e in Co. FL per Sec. per Sq. Mile^ (q) 





Stream Flo^ 

which they are applicable. Such calculations sliould, wherever pos- 
sible, be based on the known ratio of actual maximum and mini* 
mum flows on the drainage areas, or on drainage areas adjacent and 
similar thereto, and the use of a factor of safety as great as the 
importance of the local condition will warrant. Such data serves 
as the best and most conservative guide for all calculations of this 
class, 

A record of the maximum and minimum flows of various Ameri- 
can and foreign streams from the report of Mr, Kuichling, to which 
reference has already been made, is contained in the Appendix. 

Figure 86 shows a graphical representation of the actual rate of 
maximum flood discharge of these rivers and on this diagram is 
given the formulas, both graphically and analytically, for ordinary 
and occasional maximum floods as proposed by Mr Kuichling. It 
is evident that Mr. Kuichling has endeavored to represent the 
maximum flood conditions that may occur on any riven In many 
localities, the results given are much larger than the actual condi- 
tions of flow will warrant. 

In some cases the overflow of lands and property by floods, 
caused by back water or otherwise, may be prevented by the con- 
struction of levees and the installation of pumping plants for drain- 
age ptjrposes. Under such conditions both the extreme height pf 
the flood and the length of its occurrence become important and 
can be determined only by gatige observation. A graphical study 
of such data affords the best means for its consideration- Figure 87 
shows hydrographs of the high water conditions on the Fraser 
River at Mission Bridge. British Columbia. This stream is fed by 
the melting snows of the foot-hills, and the floods occur at essen- 
tially the same time each year within certain limits, as a rule reach- 
ing a maximum during May, June or July. Th& difTerences that 
occur from year to year are shown by the different hydrographs 
which represent, however, gauge heights in feet and not discharges. 
The highest record is that of the flood of June 5, 1894, of which, 
however, no hydrograph was obtained. 

94, Estimate of Stream Flow. — For the purpose of estimating 
water power no safe deduction can be made from average run-off 
conditions, although a knowledge of such conditions is desirable. 
The information that is needed for the consideration of water power 
h a clear knowledge of the maximum and minimum conditions, 
the variations w^hich occur between these limits and a knowledge 
of the length of time during which each stage is likely to occur 
n> 



M- rf^ 



Estimate of Stream Flow. 171 

hroughout the year or throughout a period of years. As pointed 
►ut in the previous section, the extreme conditions are important in 
onsidering the height of flood as influenced by spillways and 
ther obstructions in the river. The extreme and average low water 
onditions commonly control or limit the extent of the plant which 
hould be installed. 

By the illustrations already shown it is fully demonstrated 
hat the run-oflF of any stream, either for the year, period or month, 
annot be approximately expressed either as an average amount or 
s a fixed percentage of the rainfall. An expression showing the 
elation between rainfall and run-off necessarily assumes quite a 
omplex form, from which large variations must be expected. 
Vhere average amounts of run-oflF are considered, care must be 
sed to base the deduction on correct principles. In considering the 
ariation in the monthly flow of a stream, the flows of such stream 
hould be considered in the order of their monthly discharge 
ather than in their chronological order. For example: in Table 
iV, the mean monthly flows, of various streams, in cubic feet per 
>econd per square mile of drainage area are given. These flows 
ire arranged in the chronological order of the months. The aver- 
age monthly discharges of the streams are calculated therefrom, 
and are shown in the last column. An examination of this table will 
show that the minimum monthly flow of a stream docs not always 
occur during the same month for each year. For the consideration 
of these streams for water power purposes, the better arrangement 
of the recorded flow is not in the sequence of the months, but by the 
monthly periods arranged in the relative order of the quantities of 
flow. 

In Table XVI this data has been rearranged. In this arrange- 
ment the least flow for any month in a given year is placed in the 
first line and the flows for other months are arranged progres- 
sively from minimum to maximum. The average for each month 
will, by this arrangement, give a much better criterion of the 
Average water power to be expected from each drainage area dur- 
ing each year than the average monthly flow as determined in 
Table XV. 



172 



Run-Off, 



TABLE XV. 

Mean MoniM^ F7aw9 of Various Eastern Streams Arranged in ChronotSffM 
Order. (In Cubw Feet per Second per Sq^tare Mile.) 



Kennebec River at Watervilie, Me. 
Drainage Area 4380 eq miles. 



Yi*iir, 


♦03 


'u 


*ft5 


'oa 


ITT 


Ma 


1»« 


'to 


'01 


m 


'00 


IM 


m 


An. 


jAnuarr . .,,.*. * * „ 


M 


.87 


.46 


.flS 


.31 


.TS 


.53 


.,« 


.73 


.m 


J>^i 


9.« 


.1« 


,m 


PebriiAry »..«,,.. ^ «,,..,, «« . , 


.53 


.40 


.41 


.Oi 


M 


.77 


.U 


S.^> 


.57 


.«7 


.es^ 


.20 


.ao 


,'^ 


li»reh..„...., 


.\X> 


.»i 


.45 


a.fls 


M 


s.se 


.n 


ii.07 


1.10 


&.67 


4.4S! .86 


i.» 


IVJ 


65!'.::::::::::;:::::::::;;:::::::: 


ft.« 


a.^ 


5.43 


a, Si 


5.73 


«.7e 


B.31 


0,43 


B.S» 


6.07 


8.74.3.41 


3.(M 


5,11 


O.OS 


£.17 


%AT 


a.S7 


O.IO 


S.TO 


4.ai 


0.41 


nM 


a.s& 


i.ii6 4.n 


$.40 


4.17 


June .................»...«,,.,,,,, 


S.4T 


l.VJ 


I.*6 


1.^ 


S.M 


a.es 


9.00 


^.m 


IM 


3,48 


l.&S 


].!« 


1.iS 


114 


July 


l.«l 


t.ao 


,«o 


i.tti 


2. tie 


.m 


1.14 


t.ai 


1.17 


:«79 


IJtt 


1.S3 


i.r 


151 


AiifHisi , p .». , 


.ai 


.87 


.ai 


.71 


1.05 


.71 


.7» 


.AG 


.96, 


1J0 


.es 


l.OT 


.71 


.»? 


Beplembf r . . , , ^ -».-.«■**#<«* * 


.40 


(K 


.40 


.77 


1,04 


.&» 


.4{t 


.89 


.04 


.96 


.67 


M 


.« 


.fiS 


Octobef. .,».,, 


.OS 


.re 


M 


.Ba 


.eu 


.sia 


.28 


.u» 


.07 


1.3» 


.44 


1.07 


.40 


Jff 


NoT^'iTiber ........<....,. * , * 


ui 


.s& 


1.27 


9.07 


1.29 


1.77 


.46 


1.44 


M 


1.03 


.83 


.77 


M 


M 


Def-ftnber. .„,,,.,,,,„,,„ 


ae 


.44 


Kar 


.ea 


l.Sil 


.51* 


,fi1 


.Sf) 


1 rj 


.W 


*^ 


.WJ 


,47 


,7S 


Aver^^. , . . 


1.65 


M2 


1.K7 


].&4 


it.l7 


1.07 


L4« 


S.H 


1.9U 


1I.9S 


1.41 


1.68 


1 13 





I 



Merrimac Blver at Lawrence, Mass. 
Drainaf^e Area 4553 Bq. mi. 



4 




Estimate of Stream Flow. 



173 



TABLE XV.— Continued. 

Potomac River at Point of Rocks, Md. 
9654 sq. mi. 



Year. 


*D8 


■w 


M» 


M)i 


M?i3 


xia 


'W 


W 


Ave. 


Juaaaiy . . ♦*♦»*.*♦,**,*,, 


S.4n 
l.«7 

.an 

.^ 

1.45 
.H7 

t.30 


s.ou 

.ST 
1.11 


.ea 
,afl 

.81 
,30 

.u 

.14 

M 

.as 


.57 
.AT 

4,07 

9.01 
l.U 

.87 
.77 
.40 
.48 


1,Sl 
2.04 ' 

.as 

J5 

.29 

1.51^ 


l.TB 

i.aa 

1.39 
.CO 
*48 
.3S 


.78 
Ktil 
1.16 

,rr 

,S7 
1.00 

.47 

.17 
,14 


S,4^i 

.m 

,4tS 

i.tw 

.00 

.ao 

.24 

1.10 

.78 


1.8a 


Ft?bni*rr, ,« ,*, 


i.n 


JlATdl./, 


S.&S 


ApiiJ.,.** ,,.. 


ros 


J4&T»* ^...^. 


l.IB 


4hms ..,>.»*,.«««*,*,,,«■ 


.07 


Jul/ .,.».•* ,.„. 


.84 


AygiuiC.^i.*.., ...« 


,M 


SrpAmbcr 


.^ 


OvtotMT , 


.40 


December .....<.» 


.88 
1.11 


A«tt^t£V **..-**....♦*..-,* 









From Table XVI it will be seen that the average minimum 
-monthly flow of the Hudson River at Mechanicville, N. Y., is .52 
cubic foot per second per square mile, the smallest monthly mini- 
mum for any year during the period of the observations being .31 
and the largest monthly minimum for any year being .81. On the 
Potomac River, with a somewhat greater total annual rainfall, the 
average minimum monthly flow is .21, the smallest monthly mini- 
mum for the year being .12, and the largest monthly minimum for 
any year being .37. These figures, it must be remembered, are aver- 
ages for each month, and the actual minimum flow during the period 
is a much less quantity. These records show that the minimum flow 
01 a stream cannot be based on the mean annual rainfall. This same 



TABLE XVL 
^ean Monthly Flow of Various Eastern Streams Arranged in Order of their 
Magnitude. ( In Cubic Feet per Second per Square Mile.) 

Kennebec River at Waterville, Me. 
4410 sq. mi. 4380 sq mi. 



Year. 



Jl*l]mnfn ,,. p. 



*9A '^ 



.4a 

.51 

.sa 

.AO 

,flFi 

I 111 

IM 

3.47 



.4i> 
.42 

.es 

.S5 
.86 

m 

1.30 
1. 77 
2.1 
^.S3 



'OS 



.98 
.40 
.41 
.45 
.4ft 

.ei 

.BO 
i.arr 
un7 

1. 4ft 
3.17 

5.4a 



J 



I 



.03 
.04 

.71 
.77 
.88 

Lif 

> (17 



'97 



M 
.SI 

.K4 

1.04 

I. at 

\\^ 
6.10 



■BS 



43 
in 

51 
M 

n 

,V0O|2 

4.B1 

5.81 



'9» 



'00 



54 
63 

m 

93 
05 
1 31 
1.441 
I 
1 



1.07 

2 28 

!i. 70^0. 41 

e 



1.0s 

Oft 1.18 

a. 4^ 
5.0fra 

ft.&7 



S3 

44 
m 
es 

881 

S9 1 
19 T 

5^ 
8fi 
'4 



HH 



4.444.71 



"OB 



.40 
.47 
.52 

.m 

,70 

T.I 

1,07 

1.20 



m 

07 
1,0^ 

IBS 

3.419. 40 



ft. OH 



Ave. 



.48 
.116 

,efl 

.7^ 
.78 
.00 
.DO 
1.2fl 
1.S7 

4.05 
6,73 



17^ 



Run-Off, 



TABLE XVL— Continued. 

Hudson Eiyer at Mechanicvillej N. Y* 
Drainfige Aren 4500 eq. mL 



T*ar. 


•88 


*8e 


'm 


*9I 


'92 


'99 


*&1 


'OS 


'fld 


*»7 


'9S 


1?fl 


'00 


■01 


XK 


•OS 


•o* 


*» 


i 
Ate 


Uiniotum . . 


.84 


-M 


.43 


.3^^ 


63 


M 


.4U 


.57 


.&4 


.fifl 


.57 


81 


AH 


M 


.81 


.78 


.5g 




n 




J« 


.33 


.15 


.« 


.W.1 


.71 


M 


.5tt 


.dfi 


.01 


.^ 


.46 


.47 


M 




.»] 


,87 


-7» 


.# 




.C?J 


.K-f 


:;i 


.&; 


.oa 


,S1 


.70 


.58 


.&i 


,87 


M4 


,W 


.5: 


,TS1.4C1.(W 


1.03 




m 




.tta 


M 


l,&4 


.50 


1.'^ 


..tt© 


.HI 


♦76 


.»l 


M 


1,17 


.£8 


.00 


,»1.4< MS 


1.891.35 


IV 




i.«a 


1 ,iH 


1 74 


.n 


\ m 


l.O^i 


.97 


.iXr 


1,0S 


1.83 


J.^i^ 


,58 


-III 


.KK4] 


I J8 


1 Sil 


l,3!i 


ih 




LOW 


1 .'bsl 


i.^JT 


.1*1 


2M 


1,07 


1 (^ 


S7 


I.OI 


^.a- 


x.m 


i.w 


1.11 


.04 1.65 1.31 


1.4fi 


1.3J 


: i* 




hii 


1 77 


i'.Wi 


1.3?j 


■2Mti 


1 11 


K42 


.113 


i.iift 


a,4T 


1 ?2 


M7 


ua 


I mi .^-fl 


^ :'h:!t »> 


l.^ 


h*i 


M 


1 SSi 


i.m 


^,U5 


1.^ 


^Al 


i.ria 


Kfio 1 r»a 


Lfil 


IJ.ttJ 


1.7.1 


1.45! 


1.30 


1.: v.TSf 


IM 


1 7i 


■ 


2.2i 


l.l?7 


^.47 


i,tii 


ij.«0 


i.WJ 


l.m 


1. 51 


t..%4 


3.70 


if. 05 


1.4a 


1 .7-2 


1- ;^fl 


»Ofl 


soo 




$.8(1 


«.+i 


im 


^r>9 


i,i9 


i.y7 


IM^ 


l.HT 


nr.fi2 


'i.it 


ir.iti 


3 H 


3.00 


I. s, ,.,,..„-.&* 'jji 


XK 




4.7:i 


aim 


:i.a'i 


»4H 


4.f*r 


n.m 


a.47 


ii,43 


8 0*; 


3 3S0 


iM 


=f.l7 


iJ77 


^.ijii.a^U.ii a »« 


2<IT 


lit 


lid xl mum.. 


4.76 


3.04 


8,i»8 


4,45 


4.711 


4.« 


a.£8 


S.3J» 


5ft5 


4.24 


4.41/ 


5.85 


S.Cfc! 


G.23fi.5d(i.a7 4,fii 


*« 


4.& 



Merrimac ELIver at Lawrence* Maes. 
4553 ^. mi. 



Year, 


W 


*9r 


•92 


»93| 


'M 


■05 


^W 


'97 


'OS 


^90 


•00 


'01 


'OS 


w 


*04 


'flft 


Are 


MltltmWtTi .,,.,...,,. 


.69 
,76 


47 
.&4 


.47 
.8& 


.57 


.ST 
.40 


M 

.48 


.44 


:S 


:S 


M 
.44 






,74 
,81 


.81 
.64 


.30 


.4B 
.57 


-0 




» 




1.44 


.M 


.87 


M 


.44 


.57 


.er 


,75 


.88 


.4« 


.41 


flS 


M 


.73 


-57 


M 


ei» 




1 5a 


.ftfl; 


M 


,m 


.50 


.57 


,77 


t 01 


1.41 54 


.65 


.66 


ija 


.7B 


f^ 


.7^ 


,K^ 




1.7«> 


MI 


1.05 


.n 


50 


M 


.yo 


1.12 


1 4a; .61 


.74 


.ra 


tr^ 


.^0 


W 


7TI 


tr 




1.73 


.1*0 


1,00 


.?w 


M 


m 


/JS 


i.-ja 


]M .(Jl 


.87 


.88 


1,24 


.861 


.ttL> 


,83 


.W' 


^^L 


1.81 


I.OO! 


t.ift^ 


.07 


.117 


.m 


1.14 


3Sii 


1.71 


.H5 


1.;^^ 


.96 


1.64 


.W 


6» 


.«D 


11? 


P 


i.tto 


1.01 


l.*l 


1,10 


,7H 


l.iiS 


1.44 


3.2S 


1.98 


l.fr7 


1.49 


1 J>1 


1.74 


1.00 


.7*i 


iia 


14.' 




2 7." 


S.t« 


1 til 


IM7 


.9* 


1 at 


1 . Iff 


- *! 


S,17 


L73 


^2} 


SD4 


>.Tfi 


1.99 


100 


1.3K 


I.»l 




S.14 


^JVtft 


1 7B 


2.36 


1.83 


2011 


3.00 


3.117 


lA'^* 


J Oil 


S.^6 


d 09 


a.s4 


iJ.fil 3.64 


L«M 


1.10 




H.44 


1. 7a 


1.S7 


a. 4^ 


^4^ 


3.10 


4.iKl!a.79 


8,54 


^ 0^ 


:iS* 


3 tf-t 


a.?s! 


:*.S4;a.7i 


lan 


ZM 


Mudoitim.t 


3 7B 


5.10 


a.25 


1.2i 


3 10 


4 35 


4,62 3 87 


4.00 


5. til 


4.06 


4.U4 


6.05 


5.084.45 


>.c 


4«f 



Polotnac River at Pomt of Rocks, Md, 
0654 «q. mi. 



m 



Yew. 


•38 


^ 


^ 


'01 


■0^ 


m 


W 


•Ofi 


At*. 




.S6 


.25 


14 

.14 


:S 


.15 

.ao 


.30 


,ia 

,14 




Jl 




.«& 




,42 


^ 


,w 


.48 


.89 


,^ 


J7 


.sa 


.81 




.sa 


.i:7 


.81 


57 


.29 


.48 


.f& 


.4« 


.4a 




.87 


.33 


.45 


,77 


,83 


,50 


.85 


5S 


.51 




1 45 


,4e 


.4A 


.87 


.81 


.64 


.47 


,60 


M 




1.6a 


,54 


.64 


1.11 


.m 


1.^ 


Tfl 


.08 


91 




1 80 


i.so 


.88 


1.49 


l.Bl 


1,78 


.77 


.68 


IK 




1.67 


l,« 


,ett 


2.01 


i.ge 


1.86 


.97 


.«9 


1.4tJ 




1 89 


KSS 


.M 


^83 


9.S« 


a.30 


l.ftl 


1.06 


t^ 




11.84 


BOO 


t.as 


^,85 


8,37 


S.77 


1.1« 


l.tO 


«1«1 


HAxftniitD .....itti'Tt ^f ' 


2.40 


aTS 


1.9a 


4.07 


BM 


3.79 


1.81 


3.4JJ 


S.Ol 







fact is more fully demonstrated by the tables on maximum and min- 
imum run-off given in the Appendix. From the data in the Appen- 
dix it will be noted that the recorded minimum of some of the 
Southern streams is between ,5 and .6 cubic feet per second per 
square mile, while numerous other streams will vary from .2 to 4; 
nevertheless a large oortion of the streams shown have minin 
flows of ,1 and less. 




CHAPTER TX, 
RUN-OFF (Continued). 

95. Relation of Run^Off to Topographical Conditions. — The rel- 
ative run-oflf from a drainage area depends largely on its topo- 
^apliical condition. This is due to the fact that climatic condition 
depends on the elevation and slope of the drainage area, and also 
to the fact that the rapid removal of the water from steep slopes 
assures less activity in the other factors of rainfall disposal and 
consequently a greater run-off, Mr, F, H, Newell in a paper before 
the Engineering Club of Philadelphia (see Proceedings Engineer- 
ing Oub of Philadelphia, vol. 12, page 144, 1895) presents a dia* 
gram (see Fig. 88) which shows in a broad way. the influence of 
such conditions. In describing this diagram Mr. Newell says: 

"The diagonal line represents the limit or the condition when 
all of the rain falling upon the surface, as upon a steep roof, runs 
off; the horizontal base, the conditions when none of the water 



«|30 

M 

3£ 

E 

u 

t 

IS 














/ 




/ 


t 












y 




/ 


/ 




'A 








/ 




/ 


/ 




/ 








/ 




V 


^ 


/ 


/ 








/ 




y 


Z\ 


y 


y 








/L 




^ 


^ — 1 















10 15 20 23 HO 35 40 

DtPTM or MEAN ANNUAL RAll^FALU in tNCHCS 

Fig. S3 



45 



sa 



176 



Run-Off. 



flows away. Between these are the two curv^ed lines, the lower rep- 
resenting tbe assumed condition prevailing in a catchment basb of 
broad valleys and gentle slopes, from which as a consequence there 
is relatively little flow, and the upper curve, an average condition 
of mountain topography, from which large quantities of water are 
discharged* For example, with a rainfall of 40 inches on an un- 
dulating catcl ment basin, about 15 inches is discharged by the 
stream, while from steep slopes 30 inches runs off. With le^s 
mean annual rainfall the relative run-off is far less, as for example, 
with 20 inches, about 7 inches of run-off is found in steep catchment 
basins, and abont 3 inches on the rolling plains and broad valleys 
of less rugged topography* Following these curves down, it would/ 
appear that as the average yearly rainfall decreases the ruti-off' 
diminishes rapidly, so that with from 10 to 15 inches no run-off 
may be expected on many areas, and from 2 to 4 inches from the 
mountains. There is an apparent exception to this, in that with 
very small annual rainfall the precipitation often occurs in what isj 
known as cloudbursts » large quantities of water falling at a sur-l 
prisingly great rate. Under these conditions the proportion of run-l 
off to rainfall increases, as the water does not have time to sat- J 
urate the ground/' 

'These curves should not be regarded as exact expressions, but 
as indicating general relationships and as showing graphically de* 
ductions based upon long series of observations of quantities noi 
determined with exactness. Computations of this relation made 
in various parts of the country have, when platted graphically, 
fallen near or between these curves, according to the character of j 
the country from which the water was discharged. On the figure] 
are shown three average determinations, numbered i, 2 and 3, rep- [ 
resenting respectively the relation of run-off to rainfall, for the] 
Connecticut, Potomac and Savannah Rivers. The horizontal !mes 
indicate determinations made for western streams coming from | 
areas of small precipitation. The exact amount of rainfall is not 
known, as the observations are not representative of the conditions 1 
prevailing upon the mountains, and therefore the horizontal line has I 
been used instead of a dot, as indicating the probable range erf 
rainfall, as. for example, being from to to 15, or from 15 to 20 1 
inches. The height of these short lines above the base indicate*! 
the average annual nm-off of the basin, a quantity which has beeaj 
determined with considerable accuracy according ta the methnij 
just described," 




t^m 




Effects oTGeological Conditions on the Kun-i 



Figure 88 is presented on account of the general principles 
illustrated thereby and should be used for such purpose only. 
While the limits given by Mn Newell are sufhciently broad to 
include many of the conditions in the United States, they are too 
broad to g-ive a sufficiently definite relation for most local conditions 
and too narrow to include all conditions which may occur in the 
United States. The latter fact is perhaps best illustrated by Figi 
8g, reproduced from a paper by Messrs, J* B* Lippincott and S. G- 
Bennett on "The Relation of Rainfall to Run-Off in California", 
published in the Engineering News, voL 47, page 467. This fignre 
shows the annual and mean run-off from various California drain- 
age areas based on several years* observations. The diagram shows 
both the Newell curves, illustrated in Fig. 88, and three mean curves 
for California conditions, also several mean and numerous annual 
rtin-off obser%^ations which can be studied in detail in the article 
above referred to. The general curve for large drainage areas is 
for areas of 100 square miles or oven 



' 




?a m >a vi *o 4% ao 

AMNUJIL KAINPALI, IN INCHES 



ifl IB 70 7h 



Fip:, 89 



96, Effects of Geological Condition on the Run-Off, — The geo- 

lofical condition of a drainage area has a marked effect on the 
run-off. The determination of the exact geological conditions of 
my drainage area, which control or modify the resulting run-off, 
is difficult or even impossible and can seldam be done with suf- 
ficient accuracy so that the results may be even approximated with- 
out actual observ^ations on the drainage areas. The effects of these 
conditions, however, are important and they are here pointed ooit 



178 



Run-Off, 



so that such effects may be realized and the fact appreciated 
the run-off of streams otherwise similarly located may be matenall/ 
different on account of difference in these conditions. A ^ood ex- 
ample of the geological infiuence on run-off may be seen by compar- 
ing the stream flow of any of the Northern Wisconsin streams with 
that of the Rock River in the Southern portion of the state. Most 
of the Northern Wisconsin streams flow, in part, over pervious^ 
beds of sand-stone and a considerable amount of the water fallinf 
on their drainage areas is undoubtedly lost through absorption by 
the underlying strata. These losses undoubtedly affect the flow of 
the stream to a considerable extent. These streams, however, have 
no large under- flow through loose material which can absorb and 
transmit any considerable portion of the rainfall that would other- 
wise appear as surface run-off. The Rock River, on the other hand, 
follows for a considerable portion of its course through Wisconsin, 
its pre-glacia! drainage valley which is filled to a depth of 300 feci 
or more with drift material consisting largely of sands and gravels 
through which a large amount of water doubtlessly escapesi Tlie 



TABLE XVII. 

Comparative Mean Monthtt/ Run- Off of the Whemrna Biver at Nf'(^&iah Wti^ 

cons in, and the Rock River at Rock f on, IfVnou, in Cuhi<; Feet 

Per Second Ffr Square MUe. 

1903 





gd 


jS 

^ 


C 
A 

S 


< 




4) 




< 


«2 





> 


6 
it 


WUconsin river, 

Hocic river. . « * . ^ . ^ . , 


.45 


A4 


2.04 


I A3 


2,50 


L19 


1.56 
.91 


1.15 
<63 


.91 




.86 


-: 
















^ 




1904. 






Wisconsin river* 

Rrick river 


[^ 


111 


ilm 


2.21 
1.7^3 


2.63 
.8K 


1,96^ 
.39 


1.02 

.20 


,fi6 
.24 


,90 
.3^ 


2.34 

.50 


M 
.30 


li 


10OII« _J 


Wipconfiin river 

Rock river*. .-..,. 


"M 


^'M 


2.10 


2.72 
1.63 


1.91 
MO 


4,02 
L.06 


1.50 
.61 


1.05 
.41 


1.28 


.39 


M 
.40 


i 


100«, _| 


Wieconain river. 

Rock river* ■ - ■ ■ 


i'.m 


iM 


i'm 


3.90 
I AM 


.58 


1.96 
.37 


I.IS 
.38 


.90 


.S9I 


■i 


1.17 


i 




J 



4 
M 



:i 



Effects of Area on the Run-Off. 179 

deposits of this old river bed have been quite extensively explored 
for water supply purposes and yield very large quantities of water 
for domestic and manufacturing supplies. Most of the under-flow, 
however, undoubtedly passes away to an unknown outlet as tht 
modern river leaves the old valley near Rockford, 111. 

A comparison between mean monthly flows of the Wisconsin and 
Rock Rivers, as shown in Table XVII, will give an idea of the effect 
of these different conditions as shown by the run-off of these two 
rivers. 

97. The Influence of Storage on the Distribution of Run-Off. — 
Favorable pondage conditions on a watershed have an important 
effect on the distribution of the run-off, and this effect is readily 
discernible in the records of flow from such areas. 

Figure 90 is a hydrograph of the discharge of the various rivers 
draining the Great Lakes for the years 1882 to 1902. A general 
similarity is seen in the annual variations in these hydrographs and 
yet there is a considerable variation from the maximum to the 
minimum discharge in accordance with the rainfall and other condi- 
tions prevalent on the watershed. In every case, however, the 
minimum of the year is found to occur at about the same time, and 
the time of maximum height is also fairly constant. The ratios 
between maximum and minimum flow are very much less than those 
that obtain on other watersheds where the pondage area is much 
less. 

In the St. Lawrence River the maximum mean monthly discharge 
is about 320,000 second feet, and the minimum is about 185,000 
second feet, the maximum being not quite double the minimum. In 
the discharge of the Niagara River the maximum mean monthly 
discharge is about 260,000 cubic feet, and the minimum aboui 
75.000, the fluctuation being still more moderate. 

The mean monthly discharge of the St. Marys River shows a 
niaximum of about 110,000 second feet, and a minimum of about 
50,000. The ratio here is somewhat higher, because, in this case, 
Lake Superior and its drainage area being the source of supply, 
the relation of pondage to drainage area is less than in the com- 
Wned lakes, and the effect is seen in the variation in the discharge 
of this river. 

98. Effects of Area on the Run-Off. — The size of the drainage 
area of any stream has a marked effect on the distribution of the 
nin-off. The hydrographs of small areas show the effects of 
heavy rains by an immediate and marked increase in the flow* 



I So 



Run-Off. 



D 

B 

■ 

s 

"in 




i 



i 






X3 






t 

HA 




The Study of a Stream from its Hydrographs. i8i 

liis is well shown by a comparison of the. hydrographs of Per- 
iomen Creek and the Kennebec River (Fig. 96), and of the 
lood and Spokane Rivers (Fig. 99). On small streams where per- 
ious deposits are largely developed, the rainfall is rapidly absorbed 
nd does not so radically affect the run-off. Large streams do not 
jel the immediate effect of rainfall, on account of the time required 
>r the run-off to reach the main stream. The flow of large streams 
; also modified by the fact that uniform conditions of rainfall 
sldom obtain on the entire area. On large drainage areas, condi- 
ons of rainfall may prevail on one or more of the tributaries only^ 
rhile on other portions of the drainage area the conditions may 
e quite different. Such conditions may frequently be reversed, 
^ith the result that the larger the stream the less becomes the 
Ktremes of flow and the greater the uniformity of flow. 
gg. The Study of a Stream From Its Hydrographs. — ^The influ- 
nces of various factors on the run-off, as above discussed, can be 
[early seen from an analysis of the stream flow data, but they can 
est be appreciated by noting their effect on the hydrograph. The 
ydrograph of the actual flow of a stream is the best means of 
tudying its manifold variations, but to fully comprehend the wide 
imit of such variations, hydrographs must be available for a 
ong term of years. When the hydrographs are sufficiently ex- 
tended to cover all of the usual variations in rainfall and other 
meteorological conditions, they afford a comprehensive view of 
the entire subject of the run-off of the stream. 

Figures 91 and 92 show hydrographs of the Passaic River for 
seventeen years. From these hydrographs the actual variations in 
flow as they have occurred on this drainage area during this period 
can be seen. The average monthly rainfall on the drainage area has 
also been shown on these diagrams and the effects of such rainfall 
on the run-off should be noted. It is important to note especially 
the marked effect of a limited rainfall during the months of the 
storage period, when the ground has previously become saturated, 
^^ compared with the effects of the same or greater rainfalls during 
^he growing period, when the ground water has been partially ex- 
hausted by the demands of vegetation and the draft of the low 
^ater flow. 

h these diagrams, and those following, the flows are shown 
in cubic feet per second per square mile, in order that their 
value for comparative purposes may be increased. The absolute 
discharge of a river in cubic feet per second gives no comparative 



iSi 



Run-Off. 



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Figures n«Ar top of eftcb (fla|7nm show total nionililj mlnf^l. 
Fig. 92— Dally flow of Passaic Blver, Little Falls, N. J. 




184 



Run-OE 



measure of discharge values, but when the corresponding area is 
also shown, the diagram becomes more or less applicable for com- 
parative purposes to other areas. Hence, for general or com pan- 
tive discussion, the discharge per unit of area should be the basi^ 
of consideration. 

100. Comp^-ative Run- Off and Comparative Hydro graphs.— In 
studying and comparing all run-off data and the liydrographs basd 
thereon it is important to note that a uniformity of conditions pri> 
duces a uniformity of results. Such data is not only of value in 
the study of the river from which it is obtained, but also furnisher 
information regarding other streams that exist under the same or 
similar conditions, both physical and meteorological* 

Table XVI T I, which shows the monthly run-off for a term of year> 
of certain Michigan streams, gives a comparison of the flow of 
streams under such conditions, as expressed by their comparative 
monthly run-off. The relative geographical locations of these 
streams are shown in figure 93. The run-off from each drainage 
area is given in cubic feet per second per square mile, so that ttie 
results are strictly comparable, the question of size of area feeing 
eliminated. A general resemblance can be traced between most of 
these streams. The Manistee and Au Sable Rivers, in the Northern 
portion of the state, have sand and other pervious deposits largely 
developed on their drainage areas, and show, in consequence, 
greater uniformity of flow amj a greater mean flow than that of 
the other streams. 

Comparative hydrographs of some of these streams for the yea^ 
1904 are shown in Fig. 94. The vertical scale for each of the ' 
hydrographs shown on the diagram is the same, and represents the 
discharge in cubic feet per second per square mile. The relative, 
flows of the different streams are thus easily compared. On tlies« 
diagrams has also been shown the average rainfall which occurro 
on each drainage area for each month. A study of the rainfai 
record in connection with the flow lines of the h yd rograph, wil 
show that the difference in flow is not entirely attributable to tb 
prevailing rainfall conditions on the drainage area» but that otli6 
physical influences have a material effect. These hydroirraph 
were originally prepared in order to form a basis for an estiniatt 
of the probable horse power on the White River, on which fi£* j 
gauge readings had been taken- On the right of the diagram i? 
shown a horse power scale from which the probable po^ver of the 
White River, with a given fall and drainage area, and on the basis 




Comparative Hydrographs* 



i8S 




Fig, 93.— Mmp showing location of variouB MicLigac dminage 
U 



^ 



i86 



Run-0£f, 







Fig. d4. — Ckmiparative Hydrography of VarlouB Mlchlsaa ElTers for Uie l« 

1904. 



Comparative Hydro^raph*. 



187 



«V0IA4 MUM IMflaM i3»fli ItUfii 



I 

i 



a 
en 



I 
I 

i 




i 

9 



La 



S3 



d 

■a 



I 



iO ^ W €U - O 



A 



iS8 



Run-Off. 



TABLE XVfIL 
Discharge in cubic feet per second per square mile of drainage area of various 

Michigan rtwer* 



1001 
Marcli ..,.,, 

April 

May 

June 

July. 

August 

HepDettiber. . 

OcUiber 

November , . 
December . . . 



I 



1902 
JaTiimry ....... 

February 

March — 

Apnl ----., — 

May 

Juue 

July . 

August 

September 

Ociober 

November . *.»» 

Decern ber .*,.,. 

Yearly mean. 

19U3 
January ..*..., 
February * , * . . , 

March «..^ 

April .,,, 

May , , . 

June -* — ** * 

July.. 

August ... 

September « . . . . 
October........ 

November 

December 

Yearly mean. 



1904 

January 

February ,,.. 
March ....... 

April * . . , 

May , , - 

June ..*....- 






1.49 
1.18 
.63 
.74 
.51 
1.31 
.70 
.41 
.32 



.40 
.29 
Llil 
.91 
.78 
.74 
,40 
.46 
.21 
.48 
.77 
.34 
-59 



.44 

.65 

1.67 

1.16 

.62 

.44 

.4d! 

.79 
.68 
.43 

.as 

,71 



.38 

,64 

3.48 

1.17 



Grand river 


■^^ 






'^ 


'^ . 




K 


G <ii 


bb 


eS 


-1 


^1 


^ 




2 











^ es S 

-a a> tj 
^ > :i 

3Q'Cffl. 



3.25 

i.au 

.6t) 
.h9 
.92 
.38 
.39 
.47 
.42 
.66 



M 

.40: 

1 41 

1.03 

1.16 

.70 

1.57 

.53 

.5 

.79 

.95 

.96 



1.53 

2. 20 

2.13 

2-04 

.68 

.53 

.45 

.52 

l.Oti; 

l.}5 

.64 

.62 

1.05 



2.90 

1.00 

..52 



2,73 
1.06 
.48 
.34 
.78 
.68 
.44 
.61 
.35 
.66 



.65 

.43 

1.26 

1.02 
1.09 
.88 
1 78 
.57 
.50 
.84 
.66 
.62 



.83 

1.36 

2.69 

2.45 

.52 

.4^> 

.53 

.79 

1,04 

.62 

.43 

.33 

1.00 



.48 

1.07 

3.05 

3.22 

.6it 

.33 



.64 
.63 
.57 
.61 
.62 
.50 
.60 
,57 
.64 



.46 
.46 

.68 
.55 
.55 
.56 
.62 
.54 
.52 
.61 
.63 
.64 
.56 



.93 

1.20 

1.84 

1 m 

.76 

.69 

' .62 

.69 

.92 

.81 

,6S' 

.72 



.82 

.98 

3.44 

2.08 

1. 

.73 



Q * 

Es(^*j be 



« * C -J 

s s^ £ '^^ 



L29 
.76 
.53 
.45 
,38 
.54 
.71 
.70 



.69 
,62 

1.32 
.90 
.98 
.U2 

1.10 
.60 
.58 
.84 
.79 

1.00 
.86 



1.13 
1.62 
2.06 

1.76 



.41 
.66 



1.40 
1.4R 

3.07 
2.24 

.68 



.46 
.45 

.40 
.37 
.50 
.38 
.38 



.30 
.33 
.67 

i.oa 

1 34 
.77 
.04 
.47 
.46 
.67 
.57 
,54 
.68 



.67 
1.58 

1.38 
.91 



1.22 

1.40 
1.40 
1.S5 
1.28 
1.41 



1. 
1.18 
1.29 
S.36 

2,00 
1.42 






.71 
.71 
.76 
.96 

.93 



1.94. 

IM 
1.49 
1 06 






.^^ 



Comparative Hydrographs* 



189 



TABLE XVTTL— Continued, 



Grand river 

a 




dS ?* £ 



5-2 



o 

o 

N 



1- 5 

OJ *» n 
aj * § 

-a '^ ■^ 

xTP5 




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>3> Id 
> lit 



y 






3 P S 



« ^ ^ 

:sS3 



luly..,. 

Augoat 

September 

October.,,, ., 

Xovetnber 

December , 

Yearly m^an . 

Mean for Last 5 01 
6 months .^.. . . 



19(^ 
January ...^.*» *.., 

Febniary **.,,*. 

March* 

April , , , 

May 

June . . , , . 

Mean for 6 mos. . . 



.34 

.m 

.36 
.35 

.35 



,41 



,63 

,67 

1,94 

1,47 

1.4« 

2 7e 

1 49 



.25 
,24 
,21 

,3se 

.24 
.2H 
w8 

.25 



.66 
.55 
.61 
.71 

.55 

56 

1,06 



.67 



.33 
.47 

*47 
.40 



.47 



.45 
,33 
.45 
.42 
.39 



,41 



1,22 


.90 


1J8 


.85 


1,11 


.77 


l.iy 


.82 


1.09 


.76 


1,08 


1.37 


1.3t> 


KS3 


1,14 


.91 


1,20 


1,31 


1.31 


1,97 


1.52 


1.19 


1.81 


1.07 


1.51 


1^4 


i.2;i 


.98 


X.ol 


i.n 



.40 
.66 
.68 

.93 

.94 



,74 



1 34 
1.51 
1.55 
1,55 
1.47 
1 84 
1.54 



of the com para tiv^e flows of various Michigan rivers, could be es- 
timated. In Fig. 95 these hydrographs have been re-drawn, the 
daily flours being platted in the order of their magnitude. This 
form of diagram represents the best basis for the comparative 
study of stream flow for power purposes where storage is not 
considered, and where the continuous power of the passing stream 
is to be investigated. 

A careful study of Figs, 94 and 95 will show that the run-off is 
similar in streams situated under similar geographical, topograph- 
ical, and geological conditions, and having equal, or similar, rain- 
falls on the drainage area. The departure of the various streams 
fiere considered, from the average of all, gives a very clear idea of 
ifie errors which may be expected in estimating the flow of any par- 
Ijcular stream from the hydrographs of other adjacent streams, or 
from the flow of streams more remote, and which are located under 
different physical conditions, 

10 r. Comparative Hydrographs From Different Hydrological 
Divisions of the United States, — The hydrographs off streams differ 
widely in character, both in accordance with their geographical 
location and the diverse physical character of their drainage areas. 
Their geographical location afifects their climatic, geological and 




19^ 



Run-Off. 




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r^^^i^:?^:-W>>UwA^J 



ieo4 



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Creek, Nottingham. Ala.: Drainage Area, 16C Sq, MI. 
Fig. 96.— Hydrographa of AOantic and Eastern Gulf Drainage. 




I? 

CQ 

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8 



Licking Blver, Pleasant Valley, O., Drainage Area G90 Sq. Ml. 



ti^^Mi^'^n^ 



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Seneca River, Baldwinsvllle, N. Y,. Drainage Area, 3103 Stj. AIL 



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Grand River, Grand RapUs, Mich,, Drainage Area, 4900 Sq. Ml. a 

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Ftg. %1, — H^drugraphs of Ohio Yalley and St Lawrence Drainage, 



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WiscoBMUi Itlver. Necedat. Wi«., Drainage Area, 5Si' 




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YeUowatoiie River, Livingston, Mont,, Drainage Area, 3680 Sq. Mi | 



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Niobmm River, ValentlDe, Neb., Drainage Area, 60t0 Sq- Ml. 



1904 



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Rlo Grande River, l^lmtos. N. M., Drnlnage Area, 7695 Sq- MI. fl 



3; 



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8alt River, McrlXnvell, Arlt,. Drainage Area, 6260 Sq. ML 
ing tg.—Hydrosi'&pl^a ot Mississippi Y&lley^ and Quit Drainage. 



Comparative Hydrographs. 



193 



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tfjs sd 



Spokane River, Spokane, Wash., Drainage Area, 4005 Sq. MI. 




I88d 



IB88 
















Hood RSver. Tucker* Ore., Drainage Area, 350 Sq. Ml. 




%yy^y//////A'WAm^ymyy/^.m'jyjm^ 



m^A:4mYM 

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€^yAVj^/:yyAyyAy//AWA'y/M^Ay/yAyyA^yA//yAy/A'jm^ 



Kalawa River* Forks, Wash., Drainage Area, 213 Sq. Ml. 



C3 








J 


Ktrn River 


, Bakersfield, 


Cal.. 


Drainage Area, 


2345 Sq 


. Ml, 




4 






1 


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1904 










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San Gabriel River. Azuaa, Cal, Drainage Area, 232 Sq. Mi- 



Bear River. Collinston, Utah. Drainage Area, HftOO Sq. MI. 




T 



rAss^MzitX 



1804 






^22 




P 




'.4^/ywA'y. 



Walk<f*r River. Colevllle* Cal.* Dra!nngo Area. 300 Sq. M!. 
Fig. 99.^Hydrographs of Western Drainage. 




194 



Run-Off. 



topographical conditiotiSj and results in a material difference inH 
the distribution and quantity of run-off* f 

Hydrographs from the various hydrological djvistons of the 
United States are shown by Figs. 96 to gg, inclusive. For each 
drainage area hydrographs for two years are shown in order to 
eliminate, partially at least, the effect of any peculiar conditions 
which might have obtained during a single year, and to show that^ 
the hydrographs are characteristic, ^ 

103. General Conclusions,^ — A complete discussion of run-off is 
impossible in the space available in this volume. Attention has 
been called to the general laws upon which the amount of run-off 
depends, and to the similarity in flow that obtains on watersheds 
which are physically similar, also to the variations in run-off that 
occur on different watersheds due to differences in physical condi- 
tions, A 

Each stream presents peculiarities of Us own, and in investigating'™ 
stream flow the data available is seldom the same and is always 
fotund to be much too limited for a complete understanding. Only 
general suggestions can be offered for the study and investigation 
of these subjects. Attention has been directed, as clearly as pos- 
sible, to the errors which are likely to arise in the investigation of 
water power conditions by comparative study. From a knowledge 
of such errors the engineer will realize the limiting values of iiis 
conclusions, and hence should so shape his design as to effect a^ 
safe a construction as the condition will permit, and also a construc- 
tion which will bear out fairly well his conclusions at the time of its 
inception* It is evident that no exact conclusions are possible in 
these matters, and that an element of uncertainty is always pres* 
ent. A knowledge of the extent of these uncertainties and the 
probable limits of exact knowledge are as important to the engineer 
as his ability to draw correct conclusions from data which is known 
to be correct. 

LITERATURE. 

BESULTS or STSEAIC FLOW MEABUTSBWDT^TS. 

1. Annual Reporta of the Water Bureau of Philadelphia, Contain eon^| 

plete data relating: to the Perkiomen, Tohlckon and Neabamlny* 
Z, Monthly Data Relating to tlie Sudbury; Cochituate, and Mystic, ReporU I 
ef the Boston Water Board, and of the Metropolitan Water | 
Board, Boston, 
Publications of the U, S. Geological Survey contain data for the ye 
Indicated below: 



literature. 



195 



3. 


ism. 


4. 


1SS9. 


5. 


1890. 


6, 


1S9L 


T, 


18B2. 


S. 


1S93. 


B. 


1804. 


to. 


1894- 


IL 


1S95, 


12. 


1895. 


13, 


1896, 


14. 


1896. 


15, 1S97. 


le. 


1897- 


17. 


1898- 


18, 


1S98, 


19. 


1899. 


20, 


1899. 


21- 


1900. 


22. 


1900. 


23, 


1901. 


24. 


1902. 


ZS. 


1903. 


26. 


1904. 


27. 


1905. 



TeoUi Annual Report. Part 1. 

meventh Annual Report. Part II. 

Twelfth Annual Report Part II. 

Tblrteentli Annual Report Part IIL 

Fourteen th Annual Report, Part 11. 

BuUeUn No, 131- 

Sixteenth Annual Rer:>rt Part IL 

Bulletin No. 131. 

Seventeenth Annual Report Part II* 

Bulletin No. 140. 

Eighteenth Annual Report Part IV, 

Water Supply and Irrigation Paper, No. 11* 

Nineteenth Annu^ Report Part IV. 

Water Supply and Irrigation Papers, Nob. 15 and 16, 

Twentieth Annual Report, Part IV. 

Water Supply and Irrigation Papers, NoB. 27 an^ 23. 

Twenty-first Annual Report. Part IV. 

Water Supply and Irrigation Papers, Nos. 35 to 39, Inclusive. 

Twenty- second Annual Report. Fart IV. 

Water Supply and Irrigation Papers, Nos. 47 to 52, inclusive. 

Water Supply and Irrigation Papers, Nob, G5, 68 and 75, 

Water Supply and Irrigation Papers, Noi. SI to 85. inclusive. 

Water Supply and Irrigation Papers, Nos. 97 to 100. inclusive. 

Water Supply and Irrigation Papers, Nos. 124 to 135, inclusive. 

Water Supply and Irrigation Papers, Nos. 165 to 178, Inclusive. 



EIXATIOXS OF BAIXFALL A>'D STREAM FLOW. 

28, Fteley, A, The Flow of the Sudbury River, Mass, Trans. Am, Soc, C. E. 

Vol. 10, p. 225, 1881. 

29. LaweOp J. B, On tb© Amount and Composition of Rnin and Drainage 

Waters, collected at Rothamated, Jour, Royal Agric. Soc. Eng. 

Vol. 17. p. 241, 1881, and Vol. IS, p. 1, 1882. 
Si Coghlan, T. A. Discharge of Streams in Relation to Rainfall, New South 

Wales. Proc. Inst C. E., Vol. 75, p. 176, 1884. 
3L Groes, J* J. R. Plow of the West Branch of the Croton River, Trans. 

Am. Soc. C. E., Vol, S. p* 76. May, 1884. 
32. Bracliett, Dexter, Rainfall Reoelved and Collected on the Water-shed? 

of Sudbury River and Cochituate and Mystic Lakes. Jour. Asso. 

Eng. Soc, Vol, 5. p. 395, 1S86. 
33- McElroy, Samuel, The Croton Valley Storage. Jour. Asso. Eng. Soc. 

1890. 
Si* Pitigerald, Desmond, Rainfall. The Amount Available for Water Sup- 
ply, Jour. New Eng. W. Wks. Assn. 1891 
^S. Fliigerald, Desmond. Yield of the Sudbury River Watershed in the 

Freshet of February 10-13, 18S6, Trans. Am. Soc. C, E., Vol 

25, p. 253, 1S91. 
^' Talbot A. N. The Determination of the Amount of Storm Water, Proc 

III. Soc. Eng. ^ Surveyors. 1892, 



196 



Run-Off. 



37, 
ss. 

39. 

42. 

43. 
44. 
45, 
46. 
47. 
48. 
49. 
60. 
5t 
12. 
53, 

5S« 
56. 

f*7. 
59. 



Fitzgerald. Desmond. Flow of Streams and Storage in Massachosetb 

Trans. Am. Soc. C* E., Vol. 27, p» 253. 1892. 
Fitzgerald, Desmond, Rainfall, Flow of Streams, and Storage. Tnua 

Am, Soc. C. B., Vol 27, p. 304> 1892, 
Babb, C, C, Hydrography of tbe Pc omac Basin. Trans, Am, So<v C _ 

E„ Vol. 21, p. 21, 1S92. I 

Babb. C, C. Rainfall and Flow of Streams. Trans. Am. Soc C, EL. VM.1 

SS, p. 323, 1393, I 

Meadt D. W. The Hydrogeology of the Upper Mississippi Valley, and oil 

Some of tbe Adjoining Territory. Jour. Ass*n Eng. Soc,» VoM 

13, p. a29. 1894, 1 

Ruport on Water Supply of New Jersey, Geol, Survey of N. J„ Vol, %' 

1894. 
Starling, Wm. Measurements of Stream Flow Discharge of the Missis- 
sippi River. Trans, Am. Soc. C. E., Vol. 34, pp. 347-192, 1895. 
HcLeod, C. H, Stream Measurements. The Discharge of St. Lawrence 

River, Trans. Can. Soc, C. EJ, June, 1896. 
Data Relating to the Upper MlBsisstppl. Report, Chief of Elnglneera, 0^ 

S. A.. 189G, p. 1343. 
Wegmann, Edward. The Water Supply of the City of New York- Dati 

Relating to the Croton. Wiley & Sons. 1896. 
Johnson, T. T. Data Pertaining to Rain f nil and Stream Flow, Jonr. 

Wes. Soe. Eng., Vol, 1, p. 297. June, 1896, 
Chaniler, Geo, Capacities Required for Culrerts and Flood Openlnp^ 

Proc. Inst C. R. Vol. 134, p. 313. 1898. 
Pftrmalee, W. C. The Rainfall and Run-oiT in Relation to Sewage Prob- 
lems. Jour. Asao. Eng. Soc, Vol. 20. p. 304, Mch., 1398. 
Seddon. J. A. A Mathematical Analysis of the Influence of Reservoirs 

upon Stream Flow, Trans. Am. Soa C. E., Vol, 40, p. 401. 189S. 
Sherman. C. W. Run-off of the Sudbury River Drainage Area, 1S7S-1899. 

inclusive. Eng, News, 1901. 
Clark, E. W, Storm Flow from City Areas, and Their Calculation. Eng 

News, Vol, 48. p. 386, Nov. Gth. 1902. 
Pence. W. D. Waterways for Culverts. Proc. Purdue Soc, C, E., 1903. 
Weber, W. O. Rainfall and Run-off of New England Atlantic Coafit aH(3 

Southwestern Colorado Streams, with Dlscusalon. Jour, Asbo. 

Eng. Soc Nov., 1903, 
Abbott. H. ti. Disposition of Rainfall in the BasJn of the Chagrei 

Monthly Weather Review. Feb., 1904. 
Mead, D, W. Report on the Water Power of the Rock River. Chicago 

1904. Published by the Author. 



FUKJnS. 



The Flood in the Chemung River Report State Engineer, N. T., ISH 

p. 387, 
The Floods of February Gth, 1S96. GeoL Survey of N. J. 1896. p. S 
Morrill, Parle. Floods of the Mississippi River. Bui. E., U. S. Dept 0^ 

Agric. 1897. 



n 



Literature. 197 

60. Starling, Wm. The Floods of the Mississippi River. Eng. News, VoL 

37. p. 242. Apr. 22nd, 1897. 

61. Starling. Wm. The Mississippi Flood of 1897. Eng News, VoL 38, p. 2^ 

July 1st, 1897. 

62. McGee, W. J. The Lessons of Galveston. Nat. Geo. Mag. Oct, 1900. 

63. Study of the Southern River Floods of May and June, 1901. Eng. News, 

Vol. 48, p. 102. Aug. 7th, 1902. 

64. Brown, Im W. The Increased Elevation of Floods in the Lower Missis 

sdppi River. Jour. Asso. Eng. Soc., Vol. 26, p. 345, 1901. 

65. Holister, G. B. and Leighton, M. O. The Passaic Flood of 1902. Water 

Supply and Irrigation Paper No. 88, U. S. G. S. 

66. Leighton, M. O. The Passaic Flood of 1903. Water Supply and Irriga- 

tion Paper No. 92, U. S. G. S. 

67. Murphy, B. C. Destructive Floods in the United States in 1903. Water 

Supply and Irrigation Paper No. 96, U. S. G. S. 

68. Frankenfleld, H. C. The Floods of the Spring of 1903 in the Mississippi 

Watershed. Bui. M., U. S. Dept of Agric. 1903. 

69. Flood Damages to Bridges at Paterson, N. J. Eng. News, Vol. 50, p. 877, 

Oct 29th. 1903. 

70. Kansas City Flood of 1903. Bng. News, Vol. 50, p. 233, Sept 17th. 1903. 

71. Engineering Aspect of the Kansas City Floods. Eng. Rec, Vol. 48, p. 

300, Sept 12th, 1903. 

72. Murphy, E. C. Destructive Floods in the United States in 1904. Water 

Supply and Irrigation Paper No. 147, U. S. G. S. 

F0BE8T8 IN RELATION TO BAINFALL AND STREAM FLOW. 

73. Swain, Geo. F. The Influence of Forests Upon hte Rainfall and Upon the 

Flow of Streams. Jour. New Eng. W. Wks. Ass'n. 

74. Rafter, Geo. W. Data of Stream Flow in Relation to Forests. Ass'n 

C. E., Cornell Univ., Vol. 7, p. 22, 1899. 

75. Thompson, D. D. Influence of Forests on Water Courses. Scientiflc 

American Sup. No. 807. 

76. Vermeule, C. C. New Jersey Forests and Their Relation to Water Sup- 

ply. Abstract of Paper Before Meeting of The American For- 
estry Ass'n. New Jersey, June 25th, 1900; Eng. News, July 26th, 
1900; Eng. Record, VoL 42, p. 8, July 7th, 1900. 
"7. Bremner. Water Ways for Culverts and Bridges. Jour. West Soc Bngrs.,. 
VoL 11, p. 137. April, 1906. 



CHAPTER X, 

STREAM FLOAV. ' 

103. Flow m Open Channels. — The discussion of the flow of v\*ater 
in o]jcn channels in Chapter II! inchides only such channels as 
have uniform cross sections, ahgnment, and gradient and a bed of 
uniform character throughout the length considered* Such cotidi- 
tions are closely approximated in artificial channels in which the 
quantity of water flowing is under control. In such channels, and 
with a steady flow, — that is with the same quantity of water passing 
every cross section in the same time, — it is shown that: 



(1) 



w 






c vts and ihsX 



A§ = 



In natural water courses no two cross sections are the same but 
may differ in area, a, and wetted perimeter, p ; and tlie fall, h, in any 
length, I, usually differs considerably from reach to reach. The 
quantity, q, of water flowing in any such stream is also constantly 
changing. There every condition of uniform flow is lacking and 
can only be approximated for selected reaches of such streams andj 
during periods when stream flow is fairly steady* 

104. Changes in Value of Factors with Changes in Flow, — Frofflj 
an examination of equation {2) it is evident that in any channel a* j 
the quantity of water flowing, q, changes, there must be a co^^^j 
sponding change in some or all of the factors on the other side of thej 
equation. 

For steady flow in a uniform channel, s remains constant and all] 
■changes are confined to the values of a, c and r. The laws 
change in the values of c are given by Kutter's and Bazin's formu*! 
las, but are best illustrated and understood by reference to Fig* A j 
which is a graphic expression of the formula of Bazin. 

In variable flow a change in all of the factors usually accomp^*! 
nies a change in the value of q, each factor changing in accordance, 
with the physical conditions of the channel. 

The changes in the value of c, in an irregular channelp do not 1 
ways seem to follow Bazin^s law* In some cases c is even found 1 




Flow in Open Channels. 



199 



•decrease as r increases. The law of simultaneous increase in c and 
r presupposes a channel of uniform character and condition. If an 
increase in the hydraulic radius, r, in any channel is accompanied by 
a radical change in the character of its bed the law will not hold. 
It is evident that under such conditions the values of c for different 
values of r are not fairly comparative. No more uniform law of 
change can be expected under such conditions than would occur in 
the comparison of the relation of c and r for entirely different chan- 
nel sections. 

In Fig. 100 are shown the observed values of c and r for certain 
reaches of the Wisconsin River above Kilbourn, Wis. It will be 



26 















.4 

1 












99 










) 




1 








/ 




«« 












/ 


'0 






c 


/. 




20 






^ 






/ 








E 

> 


/ 

« 




18 

i 






1 
\ 


/ 


e 


i 








/ 






lA 






\ 

v 


/ 


/ 








/ 


/ 






14 

i 

y 






\ 


/ 


/ 
/ 




\ 


V 


/ 








]I8 
m 






< 


h 


/ 




y 












■ 






/ 


X 


v « 


/ 




\ 


\, 








■ 










K 










N 


> 




A 














N. 










• 


9 












c 


V. 








































10 20 30 40 SO 60 70 80 60 100 IIO 120 

VALUES or "^C. 

Fig. 100. — ^Relations of Ck>efflcient to Hydraulic Radius in Certain Reaches 
of the Wisconsin Riirer. 



200 



Stream Flow. 



noted that the value for reacnes A, D and E follow in general the 
law as established by Bazin. These are fairly uniform. On the 
other hand the values of c and r for reaches b and c seem to follow 
an entirely different law, a condition due to irregularities in the 
cross section of the reach. 

Where the values of a, p and r vary radically from section to sec- 
tion and differ materially from the values in the sections considered 
and on which calculations are based, the value of c will be found ta 
differ radically from that which the character of the bed and the en- 
tire section would indicate. Absurd values of c are a clear indica- 
tion that the sections selected are not representative. The calcu- 
lated value of c is modified by all unknown or unconsidered factors 
of the reach. The influences of irregularities in bed or section, the 
presence of unconsidered bends or changes in the gradient, and alf 
other irregularities in the channels, modify the values of c. 

Z05. Effects of Variable Flow on the Hydraulic Gradient— lo 
order to understand the effect of variable flow on the surface gradi- 
ent of a stream, and in order to realize how conclusions drawn from 
the laws of uniform flow must be modified to meet conditions found 
in natural streams, it is necessary to consider the cause of variable 
flow in a stream, the variation in channel conditions, and both the 
effect of flow on such conditions and the effect of such conditions on 
the flow of a stream. 



Bepnoot/criON of ffcco/fo of U.S.L.S. Gauge Ah.S foa MAt /7, /6SSL 

JIT 

e • 10 n 'V » 14 






D.u„i.^.T^»^i^d,p.m f^.A£f^,». ^67fk^lh^ m^i^sf ^,k^. 



Fig. 101.— Variations in Gauge Height of the St. Clair River. 



Effects of a rising or a Falling Stream on Gradient, 30i 

The surface of a stream is constantly fluctuating, not osily on ac- 
count of the variation in flow, but also on account of wind, baro- 
metric pressure and changes in the hydraulic gradient. Such 
changes occur from hour to hour, and even from minute to min- 
ute* Larger rivers, fed directly by great lakes, are 'more sus- 
ceptible to these changes on account of the broad lake area, giving 
wind and barometric pressure greater opportunity to act. Every 
stream is, however, more or less susceptible to these changes, and 
gauge readings taken daily, therefore, show only in an approximate 
way the true height of the surface of the river at the point of ob- 
ser\'ation* This is well shown by Fig, loi, which is reproduced 
from the autographic record of a gauge at the head of the St. Claire 
River. 

io6. Effects of a Rising or a FaUing Stream on Gradient. — In a 
channel of uniform section, the bed of the channel AB (see diagram 
A, Fig. 102) having a uniform slope^ all cross sections, such as Aa 
and Bb, will be alike and the wetted perimeters and the hydraulic 
radii will be identical for all sections. The fall, bx, will be uniform 
in all equal lengths, 1, of the channel, and such uniform co!nditions 
will be maintained for all regular discharges after regular flow is 
once established. 

In such channels, during changes in the stages of flow, the hy* 
draulic gradient or slope will change until uniform flo>w is estab- 
lished. In all cases illustrated in Figs. 102 and 103, the line ab rep- 
resents the hydraulic gradient which will obtain if uniform flow is 
maintained in the channel and if there be no change in the channel 
section or other conditions. The actual water surface, caused by 
variable flow, is in each case shown by the line a'b. In each case, the 
fall, bx, would be necessary to produce uniform flow from A to B 
and to assure the flow of the normal quantity of water passing the 
section Bb as in diagram A, In diagram B and C, Fig. 102, the con- 
ditions of variable flow in a uniform channel are graphically repre- 
sented. The actual flow is greater or less than the normal quantity* 
according as the gradient is increased or diminished. 

In diagram B, the conditions with a rising stream are shown. 
Under these conditions the quantity of water passing the section 
Aa is greater than the quantity passing the section Bb, by the quan- 
tity of water necessary to fill up the channel of the stream to a new 
and uniform surface gradient. The head needed to produce the flow 
past the section, Aa, is represented by the height, xx'. The total 
fall between A and B is therefore greater than that required for the 

It 



20% 



Stream Flow. 







Fig. It^. — Effects of Variable Flow on the Hydraulic Gradient of a Streaa. 




Effects of Channel Conamon^STGradienl. 

uniform flow as represented by the head bx'. This produces not 
only a greater flow at Aa, but also a flow greater than would be nor- 
mal at section Bb. 

In diagram C, Fig. 102, the conditions of a falling stream are rep- 
resented. In this case, the head at section Bb at the moment of 
observation would, if the flow was uniform, produce a normal flow 
which would require the fall, bx, to maintain it With a falling 
stream, the section AB is emptying and the quantity of water pass- 
ing the section Aa is less than the quantity of water passing the^ 
section Bb, which in turn is also less than the normal flow for the 
existing head. A less fall is therefore required to produce the flow 
passing Bb, which, with the lower slope and the same cross section, 
is less in quantity than would be the case under conditions of uni- 
form flow. This fall is represented by the height, bx', which is less 
than the height bx, required for, uniform flow by the height xx': 
consequently the slope of the river is a'b. 

From the above considerations it will be seen (see diagram D, 
Fig. 102) that a given gauge height, Bb, may not always represent 
the same flow, for the discharge, Q, is a function not only of the 
cross section, a, but also of the slope, s. A single gauge height may 
therefore represent a considerable range of flows depending on the 
hydraulic gradient which may pass through the point with a uni- 
form, a rising or a falling stream. It is obvious that the flows rep- 
resented by the hydraulic gradient, a' be', abc and a'^bc", while pro- 
ducing the same gauge height at Bb, nevertheless represent three 
di fife rent conditions of flow. 

In the establishment of the relations between gauge heights and 
floWf it is therefore important that the observed flow corresponding 
to a given gauge reading be taken during a period of essentially uni- 
form flow, for, from the above considerations, it will be seen that 
any determination or observation made %vith a rising or a falling 
stream must necessarily be more or less in error. It will also follow 
that, after a rating curve and rating table have been established, 
the gauge height taken during changes in the conditions of flow will 
be more or less in error, althonjgh such errors will equalize to a con- 
siderable extent and will, in the main, prove unimportant, 

107, Effects of Channel Condition on Gradient— The flow of 
water in a natural channel is far from being uniform and it is im- 
portant for the engineer to realize this lack of uniformity and the 
effect of such conditions upon the flow of the stream. In any chan- 
nel of uniform gradient, as AB in diagram E (Fig, 102), if at the 




204 



Stream Flow. 








Pig. 103. — Effects of Channel Grade and of Obstruction on the Hydraulic 

Gradient of a Stream. 

section Bb the coefficient c is decreased on account of increased 
roughness in the bed of the stream, or if the area of the channel, a, 
is contracted, a change in the hydraulic gradient will follow. The 
normal gradient with uniform flow would take the position ab, but 
on account of the change in conditions at Bb, the depth must in- 
crease to keep q a constant ; a must increase to offset the decrease in 
c or c must increase to offset the decrease in a if q remains constant. 
The surface must therefore rise to the point x and a new hydraulic 




Effect of Change in Grade. 



I 



205 



gradient will be established and maintained until other changes in 

the channel condition again modify the same. Between the new and 
old gradients, a transition curve will be established extending both 
above and below the point at which the change in condition takes 
place to some point, y, frequently a long distance upstream. 

The opposite condition is shown by diagram F, Fig. 102. In this 
diagram the effect of an increase in the coefficient, c, of the bed or 
in the area, a, of the stream is represented. If c increases, a less 
section will be required below that point and again the surface Is 
lowered ; or if the width of the stream increases, the depth will 
diminish in order that ca may remain constant. 

Variable Bow is also caused by a sudden enlargement in the 
river section or by a discharge of the stream into a larger stream or 
into a lake or pond. Such conditions are shown by diagrams G 
and H, Fig< 102. The character of the transition curve in such 
cases will depend on ^ the height of the surface of the water into 
which the stream is discharged. If the water surface of the lake 
is above b, the curve will be concave upward (see diagram G) and 
if the surface is below b, the curvature will be dofn^'nward (see dia- 
gram H). 

108, Effect of Change in Grade and of Obstmctions. — Variable 
flow may also be caused .by changes in the slope of the stream bed 
as shown by diagrams A and B, Fig* 103. The area of the stream 
must increase as the bed slope is decreased, or must decrease as 
the slope of the bed is increased in order to fulfill the conditions of 
equation (2), 

It is evident that uniform slope may be maintained even with 
changed conditions if the changes that occur give rise to equal and 
opposite effects* For example, uniform slope may be maintained 
if the area of section a is reduced and the coefficient c is increased 
to such an extent that tlie product ac remains constant at each sec- 
tion of the channel. 

Variable flow is also caused by the passage of the stream over 
weirs or dams and the effect on the gradient will vary as shown by 
diagram C and D, Fig. 103. Variations may also be caused by a 
change in the bed (see diagram E, Fig 103), or by local contrac- 
tions, submerged weirs or other obstructions as shown by dia- 
gram F, Fig. ro3. 

In all of the above described cases it is obvious that if the slope 
of the stream is measured on any of these transition curves, a false 
idea of slope will obtain and a false relation will be established for 




^^^ 206 ^^^^V Stream Flow. ^^| 


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GAUCE HEIGHTS AT KILQOURH. ■ 


Fig, 104.— Relatloni of Guage Heights at Vaj-louB StaUous on the Wiscon-fl 


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Effect of Change m 



the condition of stream flow. It is therefore essential in any meas- 
urement of a stream or in the 'establishment of any gauging station 
that the location for such observations be carefully selected on a 
reach of the stream where conditions of essentially uniform flow 
prevail and that all observations be taken during stages where the 
flow of the stream is practically constant- If gauges are established 
at various points along the course of a river and are read simultan- 
eously, and if the flow is uniform and no falls, rapids or tributaries 
intervene, the same diflFerences in elevation should always obtain 
with the same stage of water, 

A system of gauges as described above was recently established 
at Kilbourn on the Wisconsin River in order to determine the river 
slopes near that place, A large number of practically simultaneous 
readings were taken in order to determine the relations between the 
gauge heights at the various points compared with the Kilbourn 
gauge. 

Fig. 104 shows the results of the gauge readings at the various 
stations compared with the gauge readings at Kilbourn. It will 
be noted from the diagram that the slope of the river was far from 
uniform at different times during these readings, and, in a number 
of cases, the same gauge reading at Kilbourn was accompanied by 
readings at other gauges that differed from each other by more 
than a foot. For example, compare the gauge readings at Kilbourn 
with the readings at gauge No, 5. With a gauge reading of 17 ft* 
at Kilbourn, the normal gauge reading at No* 5 should be 23 feet, 
and with a normal flow, the fall between gauge No, 5 and the Kil- 
bourn gauge would be 5 ft* From the diagram it will be seen that 
during a certain stage of flow in the river the gauge reading at 
gauge No. S» with a 17 foot reading at Kilbourn, was about 22^ ft. 
Under these conditions the fall between gauge No. 5 and the Kil- 
bourn gauge was only 4^ ft. The slope being reduced, the quantity 
of water actually passing the Kilbourn gauge under these condi- 
tions was less than the normal flow for the 17 ft. gauge height. 
On two other occasions where the gauge reading at Kilbourn was 
approximately 17 feet, the actual gauge reading at gauge No. 5 was 
about 24 feet. During these conditions the actual fall in the river 
between gauge No. 5 and the Kilbourn gauge was 5 feet, or one 
foot more than normal. Hence the quantity of water flowing by the 
Kilbourn gauge at this time was more than the normal quantity 
indicated by the Kilbourn gauge. 

Readings of other gauges compared with the Kilbourn readings 




308 



Stream Flow. 





will show that at certain times the flow 
was normal and at other times the river 
I must have been rising or falling and thata 
T consequently the gauge at Kilbourn at the 
time of such reading, was not accurately 
representing the quantity of water flow* 
ing by the Kilbourn section. The above 
example taken of the variation in slope 
between the Kilbourn gauge and gauge 
No. 5 indicated practically the maximiini 
abnormal conditions. The actual varia* 
tion in flow at Kilbourn during these con- 
ditions was not determined and is not 
definitely known, 

109. Relation of Gauge Heights to 
Flow. — The area of anj crot.s section 
equals the product of the height of tbe 
section into some function of its width: 



(3) 



a = h X f (w) 



In a rectangular cross section f=i, (see A, Fig, 105). In a tn- 
angular section, f=.5 (see B, Fig, 105), In all cases of regular sec- 
tion f can be mathematically expressed, and for irregular sections 
(see C, Fig, 105) the relation may be obtained by measurement 
If the height of the surface is referred to a gauge height, H, the 
zero of the gauge may or may not correspond with the bottom of 
the channel. If H=the gauge height, then h— -H+e, in which e h 
the distance from the bottom of the channel to the bottom of the 
gauge. Substituting, therefore, the value of h in equation {3) ^t 
becomes : 

(4) » = (H -f e) X fCw) = Hf(w) + eftw), 
And substituting this value in equation (2) it becomes; 

(5) Q = Hf(w)ev^ra +er(w)cv^ri" 

With this equation p and with the flow in a fixed and uniform cban- , 
nelp if the relation can be established between r, s, c, e, w and f 1 
each gauge height, H, the correspondmg value of Q can be deter-j 
mined. As these relations are mathematically expressed for wni-j 
form flow by the above equation, they can also be rcprcsente 
graphically by a curve which will show the relation between Q anil 
H for all conditions of uniform flow that obtain iti the given chan 




Relation of Gauge Height to Flow. 



209 



ncl. Such a curve is called a discharge or rating curve. This equa- 
tion (5) can be readily solved when f is a regular variable and when 
c, r and s can be determined. Where the function, f, is an irregular 
variable, no mathematical solution is practicable but the relations 
may be determined experimentally and can be expressed by a rating 
table or graphically by a rating curve. Such a rating table and curve 
can be constructed for every fixed channel or section of a stream 
for condition of uniform flow, no matter how irregular the section 
or how the values of the function of the section may vary for differ- 
ent gauge heights. 




Discharge in Cubic Feet per Second. 
Pig. 106. — ^Rating Curve for Wisconsin River at KHbaum, Wis. 

Fig. 106 shows a rating curve established for the Wisconsin River 
^tKilbourn, Wis. The small circles show the flow relative to gauge 
height at the time the observations were made. They Wfere care- 
Wly made in a fairly satisfactory section and fall fairly well on a 
smooth curve drawn from this data to represent the relation of 
gauge height to flow at similar or intervening heights. 

The character of the rating curve for regular and irregular sec- 
tions is shown by Fig. 45, page 95. Whenever the section remains 



3IO 



Stream Flow. 



similar for different gauge heights, the rating cun^e will be a smooth 
curve, but when irregularities occur in the section, the curve be- 
comes broken more or less according to the extent of the irregu- 
larity< 

It has already been pointed out that any change in the cross sec- 
lion of the stream after a rating curve has been established will 
necessitate the establishment of a new cur^^e. The variation in rat- 
ing curves under variation in channel conditions is shown in Fig, 46, 
page 0. 



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Cross-section of 
Omnha, Neb.* 



Missouri 



near 



The actual change in channel conditions that affects the relationM 
of head and flow is well illustrated by Fig, X07 which shows the T 
changes that actually took place in the cross secticm of the Missouri 
River near Omaha ^ Nebraska, 

no. Variations in Velocity in the Cross-section of a Stream.— ' 
The velocity of flow of a stream varies greatly at different points in- 
any cross section. In any channel the friction of the sides and bed^j 
reduces the velocity of that portion of the stream in contact and . 
adjacent to them. If the bed at different points of the cross-section' I 
is not uniform, as is always the case in the beds of natural streams, [ 
the retarding effects on different portions of the stream varies, andl 
a consequent variation in velocity results. The distribution of ihft I 
velocities in the cross section of the St. Clair River is shown in Fif*j 
108, both by lines of equal velocity and by figures giving the ve-" 
locity as actually measured. In this figure the effect of the frictiotKj 

•Todd. Bull 158 U. S, Geol Surv, 




Variation in Velocity in the Cross-Section of a Stream. 211 




Secfion 



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Fig. 110.— Vertical Velocity Curves, Section Dry Dock. 



:2I2 



Stream Flow* 





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r^"^-^.^ of the bed and banks is clearly shown. 

/ '^^^ The friction between the stream sur-, 

/ \ face and the atmosphere is th 

I \ shown by the fact that the maximmi 

\ velocity is not at the surface btit is 3 

^ short distance below the surfacej 
The surface velocity may be modified 
radically by the direction and velocittl 
of the wind, 
\ ;^^^^^^HH|^HHK Fig. 109 shows the transversej 
' ""^^ ctirvx of mean velocities in this m 

tion. The distribution of velocitifl 
* in each vertical section is shown iirl 

Fig, 1 10* The velocities here showitj 
^^^^ 2ire relative only as compared witliJ 

i "^ — -.^ each vertical. The %^elocity at tlie 

j \ .bottom of each curve is that shown 

I ^ by figures in Fig^. 108. 

/ V i^ ^^^^ distribution of velocities mJ 

oRoiNAftY itfATCft \^ ^^y scction is not the same under afll 

conditions of flow but differs mater- 
ially with the stage of the river, Tln^ 
y^ 'W^M is illustrated by Fig, 1 1 1 in which H 

'---:'"' shown three sections of the same 

B stream illustrating conditions of low. 

medinni and high water* Above eacli 
f^s^ section is shown a correspondiTig 

/ N transverse curve of mean velocities 

I \ of flow* The change in the distdbu- 

/ ^^/ "^ M *^*^" ^^ velocities as the stream ifl' 

! LOW WATCR \& creases should be noted. 

-. - -jp^^ -J'^¥$ The distribution of velocity is al^ 

/' '^' .'^ a flfec ted by bends in the stream above 

y _^MStL the point of observation which tends 

^'^^^^ to throw the current of the stream 

^ toward the concave side, and to cause 

^' ■ a transverse slope in the section <^^ 

the stream at the curv^e. Such a condition {see Fig. 112) creates 

cross currents and eddies and produces conditions of variable flow. 

From Fig. 108 it will he seen that in any vertical line in a given 

section, the velocities will vary with the condition of the bed, and 




Variation in Velocity in the Cross-Section of a Stream. 213. 




Fig. 112. 



CALM 



WMD D0Wlt8T WEAM W WD UP tT REAM ICE COVERED 



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PER CENT OF MEAN VELOCITY 

Fig. 118.— Ideal Vertical Velocity Curves. 



100 




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PCR CKNT OP MEAN VELOCITY 

Fig. 114.— Mean Vertical Velocity Curves. 



^m 314 Stream Flow. V 

^H the influence of air current or ice at the surface. These conditions 
^B liave an influence on the velocities in each section considered. Van- 
^H attons in the vertical velocities can be better studied by means of the 
^M vertical velocity curve, which can be obtained by means of velocity 
^m observations taken in a vertical line from the surface to the bed of 
^B the stream. Ideal curves under various conditions are illustrated by 
^1 Fig. 113. Figs. 114, 115 and 116 are reproduced from the report of 
^m the State Engineer of New York for the year 1902. These diagrams 
^1 show comparisons between the mean vertical velocities of streams 
^B having different classes of beds. From these illustrations it will be 
^M noted that there is a general similarity between the varioos velociiy 
^m curves which aids materially in the measurement of stream flow. It 
^K will he noted, for example, that the mean velocity, in any vertical 
^M velocity curve from an open channel, lies near the point of .6 total 
^H depth but that with varying conditions this position may vary from 
^B 55 P^^ cent to about 75 per cent, of the depth- The velocity at .6 
^m depth is found to average nearly 100 per cent of the mean velocity, d| 
H t>ut may actually vary from 95 per cent, to 105 per cent, of the mean 1 

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Fig, UB.— Mean Vertical Velocity CurveB. 





Effects of Ice-Covering on the Distribution of Velocites. 215 








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Fig. 116. — Mean Vertical Velocity Curves. 



velocity. The velocity at the surface is subject to the external influ- 
ence of atmospheric currents and is not so constant in its relation to 
^hemean velocity. The surface velocity will average about no per 
cent of the mean velocity of the vertical curve, but is found to vary 
^th the variations in conditions from 105 per cent to 130 per cent 
^^ such velocity. 

ni. Effects of Ice-Covering on the Distribution of Velocities. — 
The effect of the formation of an ice sheet over a stream is to ma- 
terially increase the surface friction and results in a rearrangement 
^ velocities in the cross section. As the ice sheets form in winter, 
the conditions will vary from that of an open stream to that of a 
closed channel. The velocities are gradually affected as the ice be- 
gins to form, until the entire surface is affected where the stream 
)ecomes entirely covered. As the ice sheet thickens more of the 
ross section of the stream is occupied by the ice sheet, and greater 
fiction results. Fig. 117 shows two vertical velocity curves, one for 
n open and one for an ice-covered channel. These may be regarded 





^ Stream Flow. 


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117. — ^Comparative Mean Vertical Velocity CurveB for Open and 
Covered Section. 

rpical of open and closed conditions between which the acti 

;ities will vary with the conditions of the ice, 

le change in the distribution of velocities results in an ent 

ge in the relation between gauge height and flow so that t 

g curve for an open section will not apply to the river um 

on di tions. 

therefore the stream flow is to be accurately determined duri 

condition, it becomes necessary to establish the new relati 

een gauge height and flow. 

i before noted, such relations vary somewhat with the con 

of the ice sheet but may be regarded as fairly constant wl 
ection is fairly clear and deep. The relations between the f 
curves for this open channel and for ice conditions as dct 
d by the United States Geological Survey for the Wall 
r at Neupaltz, N, Y, is shown in Fig, Ii8. 
tble XXI, from an article by F. A. TilHnghast (see Engim 
C^ews, May nth, 1905), shows the relations of maxifnum 


1 



Effects of Ice-Covertng on Velocities, 



217 



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eoDO 



40X10 soao eaoo 

EMSCKAAaC IK CUMG FEET rER flfCONO. 



Fig. lis.— Rating Curve for Wallkill River at Newpaltz. N, Y. 



mean velocities in the verticals. It should be noted that there are 
two points of mean velocity under ice conditions that average ir 
per cent and 71 per cent, of the total depth below the Surface, The 
point of maximum velocity is at an average depth of 36 per cent, of 
the total depth of the stream and averages T19 per cent, of the mean 
velocity. 

TABLE XXI. 
Pxymxiion of jlfcan a-nd Maximum Veloeitiea in a Vertical Plane Under lee. 



Stream and Place 


Depth from 
Under Sur- 
face of Ice 
Feet 


Num- 
ber of 
carves 


Depth of 
Mean 

Velocity 


Depth 

of 
Maii- 
tniim 
Veloc- 
ity 


Coeffi- 
cient 
to re- 
duce 

Mfl3t. 

to 
Mean 


Wallkill at Netjpalt^c. N. Y. , . . (a) 
WallkiH at Neupaliz, K. Y, . . .(b 
Reopnf at Kinj^tton, N. Y, . . . . . (a) 
Empua at Emp^ton, N. Y. . . . , . ( b 
Kondoutat Roeeudale, N. Y, , .(« 
Rondoat at Roaendale, N. Y. , .(b) 
C^nuvecticut at Orford, N. H. , . (c) 
Mean .......,•,,« 


4 to 12 

4tcil9 

2.3to7.4 

5to8 

4toa 

5toT 
2.5 to 7, 7 


20 

2S 

16 

8 

6 

8 

18 


0.12 
0.13 
0.08 
0.11 
0.08 
0,13 
0.11 
O.U 


0.71 
0.74 
0.68 
0.73 
0.08 
0.21 
0.69 
0.71 


0.3F 
0.38 
0.36 
0.37 
0.35 
0.35 
0.35 
0.36 


0.86 

0-88 
0.80 
0,86 
0.82 
0.85 
0,86 
84 











Kotes: a. By F. H. Tiliinghast. 
b. By W. W. Schlechl, 
c* By a A. Holdeii. 
13 





CHAPTER XL 

THE MEASUREMENT OF STREAM FLOW. 

112, Necessity for Stream Flow Measurements. — In order \n 
ascertain the value of a stream for water power purposes, it is neces- 
sary to determine the amount and variations in its continuous flow 
either by comparison with the flow of other streams or by the direct 
observation of the flow of the stream itself. As has already been 
showuj the latter method is by far the most satisfactory as the de- 
termination of the actual flow of the stream eliminates all errors of 
comparison, and the necessity for any allowances or modifications 
on account of differences in geological^ geographical, topographical 
or meteorological conditions on the drainage area. 

The Hydrographic Division of the United States Geological Sui^ 
vey has undertaken the gauging of a large number of streams in ih^ 
United States and has established numerous gauging stations 3t 
which observations have been made for a number of years. This 
data J references to which are given in the list of literature appended 
to Chapter IX, is of great vahie for comparative purposes. It iS_ 
seldom, however, that, when a stream is to be investigated for waia 
power purposes, flow data, at the particular point under consider* 
ation^ is available* One of the first duties of the engineer, ther«j 
fore, usually consists in making measurements of the stream flo 
and establishing stations at which the daily flow can be observe 
and recorded. 

The methods in use by the United States Geological Survey ii^ 
the result of much study and investigation and probably represen 
the most practical methods for making such observ^ations with a i 
degree of accuracy. Many of the methods and suggestions in th 
chapter are based on the methods and conclusions of the Surs'cy I 
modified by the experience and practice of the writer,* 



fail 



* Thase methods are described In detail in Water Supply and IrrlgaU 
Papers No 94, entitled^ "Hydrographic Manual of the United States G^ld 
cal Survey/' and No» 95, entitled **Accuracy of Stream Measurements." 
also "River Biaeharge" by J. C. Hoyt and N. C* Grover, — John Wiley 
Sona, 1907, 




Methods for the Determination of Flow. 219 

1x3. Methods for the Estimate or Determination of Flow in 
pen Channels. — ^There are three general methods of estimating or 
itermining the flow of water in streams with open channels. 
First— By the measurement of the cross section and slope and the 
Jculation of flow by Chezy's formula, together with Kutter's or 
azin's formulas for estimating the values of the coefficient. 
Second — By means of weirs or dams of such form that the coeffi- 
ent of discharge is known, and 

Third — By the measurement of the cross section area and the 
slocity of current passing through the same. 
The method which should be selected for any particular location 
spends on the physical conditions of the problem, the degree of 
:curacy required, the expense which may be permissible and the 
ingth of time during which the record is to be continued. 

114. Estimates from Cross-section and Slope. — Chezy's formula, 

V = c Vts 

Dgether with the formulas of Kutter and Bazin, for the determin- 
tion of the flow of streams, has already been discussed in Chapters 
II and X. Much information is now available in regard to the 
'alue of the coefficient c, but this value varies greatly in different 
treams, in accordance with the conditions of the beds, and in the 
ame stream under various conditions of flow. The results obtained 
rom the application of these formulas are therefore necessarily very 
ipproximate. The method, however, is of considerable value in es- 
imating the flood discharge of streams and in obtaining an approxi- 
nate knowledge of flow under other conditions where other methods 
ire not available or are difficult of application. 

In using this method two or more cross sections of the stream 
ihould be measured on reaches of the river where the cross section 
ind other conditions are fairly uniform and can be readily deter- 
nincd and at a time when the flow is steady. It is also important 
hat the stream in which the flow is to be estimated shall be compar- 
ble in cross-section, depth, and other conditions, on which the 
alue of the coefficient c depends, with other streams on which the 
alue of c has been determined. 

115. Weir Measurement — Where dams are so located that they 
m be utilized for weir measurements, and are so constructed that 
ich measurements are reasonably accurate, or where suitable weirs 
n be constructed from which such measurements can be made, 
ch dams and weirs afford the best practicable method for measure- 



220 



The Measurement of Stream Flow. 



ments of the flow of a stream, la order to assure accurate results in 
weir measurements, the following conditions must be fulfilled: 

First — The dam or weir must have sufficient height so that back- 
water will not interfere with the free fall over the same; otherwise 
the dam will be available for purposes of measurement only during 
stages when no such interference exists. 

Second — The dam or weir body, must be so constructed that no 
leak of appreciable size will occur during the time when it is utilized 
for measuring purposes. 

Third — The abutments of the dam or sides of the weir must be so 
constructed as to confine the flow over the dam at all stages: other- 
wise the weir will be useless for measurements during flood condi- 
tions. 

Fourth — the crest of the weir must be level and must be kept free 
from obstructions caused by floating logs or ice. 

Fifth — The crest of the dam or weir must he of a type for which 
coeflficients for use in the ordinary weir formula have been deter- 
mined- (See Chapter IIL) 

Sixth — If the dam has an adjustable crest» great care must be used 
to prevent leakage along such crest and to keep a complete and 
detailed record of the condition of the crest during the time of the 
observations. 

Seventh — If water is diverted around the dam, which is usually 
the case when a dam is built for power purposes or for navigatior), 
the diverted water must be measured or estimated and added to the 
amount passing over the dam* Such diverted water can sometimes 
be measured by a weir or current meter. When such water is use*i 
in water wheels, an accurate record of the gate opening of the 
wheels can he kept, from which the amount of water used in thf 
wheels can be estimated if the wheel's discharge has been calibra^eij 
or if the wheel is of some well known type,* The conditions for the 
accurate determination of weir discharge should be such as not to 
involve the use of low heads of less than 6'' over broad crested dams. 

Measurements by means of a weir or dam have the general acKati' 
tage of continuity of record during the periods of ice and flood and 
the disadvantage of uncertainty of the coefficient to be used in the 
weir formula, of complication by the diversion of water around the 
dam^ and the interference of flow by the occasional lodgement of 
material, or of injury to the crest. 



• See Water Supply and Irrigation Paper No. 180. — Turbine Wmter WN 
Tests and Power TablaBr— by R. E. Horton. 





The Use of the Current Meten 



221 



Hurement of Flow by the Determination of Velocity. — 

of a stream, or the quantity of water flowing past a 
I of the stream in a given timej is the product of two 
le area of the cross section ; and second, the mean 
' through said section, 

tlie cross-section of the stream were uniform the 
the flow would be a simple matter, A surface float, 
given stations, or a current meter placed at any 

s-section, would then indicate the average velocity. 
If however, never obtain* It is therefore necessary 

mean velocity of flow in the section which is a 

jtt matter, 

of measuring the velocity of a stream are in use: 
le of a current meter, and second, by the use of 

these methods has advantages peculiar to itself, 

knosvn and appreciated in order that intelligent 
nay be made* 

of the Current Meter.— The current meter (Fig. 
^t:nent designed to revolve freely with the current so 
lining the number of its revolutions the velocity of 



1C€ Electric Current Meter with Buzzer. 



322 



The Measurement of Stream Flow, 
Section A- A 





Flf, 12(J 



Section of small Price Electric Currenl Meter, ShowlBi 
details,* 



the current will be known. A well made current meter carefuH| 
maintained and frequently rated is reasonably accurate when prop 
erly used under conditions to which it can be applied. As the fno 
tion of operation is rarely constant ^ the relation of current velocitie 
to number of revolutions is not always strictly proportional and iti 
necessary to determine the relation between the revolutions of \hi 
meter and the corresponding velocity of water. This is accomplisliea 
by rating the meter, which is usually done by passing it throisg 
still water at known velocities and noting the results* It is assume 
that the same relation wifl exist between the revolutions of 
■meter and its longitudinal velocity through still water and bet we 
its revolution and the velocity of flowing water when this meter! 
held in a similar position in a stream. The meter should be ratd 
under conditions as nearly similar as possible to those under whic 
it was, or is to be, used. The meter when being rated is usually ; 

•From W. S. & T. Paper No. 94 Hydrograplilc Manual, by E. C. Mu 
J, C. Hoyt and G. B. HoUtiter 



k 



Current Meter Observations. 



223 




Fig. 121.— Current Met&r Rating Station at D«flTer, CoL* 



ched to some movable device (see Fig. 121) such as a carriage or 
sat which is propelled by hand or machinery at a known rate over 
fixfd distance* Observations of the revolutions of the meter at 
irious rates of speed are noted and the relation is then established 
ctween the velocity of the meter and the revolutions of the meter 
fhcel. This data may be platted upon cross-section paper or so 
ganged in tabular form that the corresponding velocity may be 
Piediately ascertained when the revolutions of the meter are 
Hown, (See Fig. 122.) Experiments have shown that with veloci- 
l&less than one-half of a foot per second little or no dependence 
■ be placed upon the meter observations and that for velocities 
TOW one foot per second, the meter usually tinder registers. Where 
iich low velocities obtain, float measurements are believed to be 
tore accurate* 
18, Current Meter Observations and Computation. — On account 
great variation in velocity at different points in the cross-sec- 

im Hydrographlc Manual. 





■ 224 


The Measurement of Stream Flaw- 


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I tion 
the 
able 
tion, 
into 
velo 
sect] 
vert 
usua 
usua 
usua 
hori 
disti 
ciira 
usee 
grea 
mor 


VELI 

Fig. 122.- 

, the flow through ai 
flow through other 
, in order to systems 
as well as for ease ir 
parts, both horizont 
city of each of said 
ion of the stream s! 
ical sections, chosen 
Lily five feet or mo 
illy somewhat less ai 
illy much greater tha 
zontal and vertical 
'ibution of velocity 
cy required in the d 
[ in the deter minatio 
ter the number of « 
e accurate will be th 


tClTY.' 
--Curi 

ny ur 
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iticat 
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totild 
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re ai 
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eas. 
rvey 
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be c 
urpoj 
but t 
tions 
ontal 
?penc 
>ss-sc 
on of 
elocit 
ivisic 


r i ■ Id 1 
.R SECOND 

iatlng Curve. 

may vary more or \k 
On this account it 
the velocities in a ci 
divide the cross-sect 
lly, and determine th 
isis for the work, th 
>btaincd by soundin 
ie of water observal 
he horizontal divisi 
in the vertical veloc 
velocities. The size 
s on the irregtilarit 
ction as well as on 
flow. The greater 
ies in the unit areas 
ms of the cross-sec 


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ESS fr 
is dc3 

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I 



Current Meter Computations. 



225 



The meter readings may be made in one of four ways : 

First — By determining the velocity at frequent, definite intervals 

depth and then ascertaining the point and amount of average velo- 

ty in each vertical section. 

Second — By what is known as the integration method, which 

nsists in lowering and raising the meter with uniform motion 

Dm the surface to the bottom of the vertical section and noting the 

^erage velocity determined by this method. 

Third — By making a point measurement at the depth correspond- 

g to the thread of mean velocity as determined in the first method. 

Fourth — By determining the velocity at some other point of 

)scrvation and deducing the mean velocity from the known rela- 

on of the point measured to the point of mean velocity. The last 

vo methods can be safely used where the vertical velocity curve 

as been determined with sufficient accuracy, and are fairly approxi- 

late at other sections where the conditions are not of an unusual 

ature. 






i 


fie* rrom MUai point 


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% 123. — Cross-section of Saline River at Guaging Station near Salina, 

Kans. 



"Fig. 123 shows the cross section of the Saline River near Salina, 
Kan., on September 30th, 1903, while the discharge measurements 
•ccorded in Table XXII were being made. The soundings were 
^ken at each 5 feet of width from the initial point and the velocity 
vas observed at 0.6 depths below the surface in each of these verti- 
als. 

The discharge through each 5-foot strip might be computed sep- 
rately, but the computations are shortened by finding the discharge 
irough each double strip at a time." 

♦ From Water Supply and Irrigation Paper No. 94, — Hydrographlc Manual 
B. C. Murphy, J. C. Hoyt and G. B. Hollister. See page 46 et seq. 



226 



The Measuremeot of Stream Flow. 



= me&n depth for double strip; 
^ =s mean velocity for datible itrip; 



Letd' 

ft, bt c are three conHecutive depths, L feet ^part^ 

V^ V^ V^ are observed velocities in the 

L = the width of a single strip; 

Q' 1=: the diecharge through double etrip. 

"The mean depth and the mean velocity for the double strip olj 

width lo feet are found from the formula : 



a> 



m 



d^„ = 



a + 4b + c 
6 






The discharge through the double strip is , 



(3) Q' = d'„ V'„ 2L 



= (- 



+ 4b + e. 



a 



-) ( 



V^ + 4V, + \\ 



Formulas (i) and (2) are based on the assumption that the! 
stream bed is a series of parabolic arcs, also that the horizontal v^| 
locity curves are parabolic arcs, both of which assumptions arc] 
approximately true at good current-meter stations. 

In computing the discharge and the mean depth through a] 
single strip near the stream bank or a pier the mean velocity is | 
found from the formulas ; 



W 



(6) 



V^ = 



d = 



a' -fa 



where cither Vo or Va and a' or a may be **0*'. 

Velocity is computed to two places of decimals, mean depthtl 
area, and discharge to one place of decimals for streams of Drdinaryl 
size ; for small streams with hard, smooth botton, where depth caflj 
be measured to hundredths foot, the mean depth and area should I 
computed to two places of decimals and the discharge to one pbc^" 

These observations can be taken in shallow streams by wading 
or from a cable car (see Fig. 124), boat or bridge as the circun^ 
stances and conditiottis permit. A rope or cable, marked into sufe 
able divisions and stretched across the stream, offers the best mean 
of locating the horizontal points at which observations in the vcri 
cal planes are to be made. 

119. Float Measurements. — Where a single or only au occasioni 
measurement of the flow of a stream is to be made, the use of floatl 



CurreDt Meter Measurements. 



327 



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The Measurement of Stream FloWi 



Is believed to be preferablei as tinder such conditions the caHbrati 
of the current meter and the exercise of necessary skill in its use are 
not apt to receive proper attention. Under such circumstances, 
therefore, float measurements are believed to be more accurate* 

In the use of floats the writer usually selects round soft wood one 
to two inches in diameter and in various lengths, varying by about 
&^. These are weighted at the lower end, usually by attaching pieces 
of lead pipe so that they will float with only about one to three 
inches of the rod exposed. To the exposed end is usually attached 
small red or white streamers so that they may be readily seen and 
yet not be seriously affected by wind* 

A point for the gauging is selected where the stream Is fairly 
straight and uniform in section, and ropes, wires, or cables are 




Fig. 124.^Cable Station, Car Guage, etc. 

stretched tightly across the stream, parallel to each other and 25, 5o| 
or 100 feet apart, as the location and velocity of the stream seen 
to demand. The ropes or wires should be tagged at intervals of J 
10 or 25 feet, as the conditions seem to warrant, beginning at zcroc 
the straight bank. 

In starting the work a float is selected that will reach as near th 
bottom as possible without torching and should be about ,9 deptll 
The float is started 5 to lo feet above the upper line and so place 
that it will pass as nearly as possible under one of the tags, 
point at which it actually passes under the line is noted and 
corded, also the point and time at which it passes the lower Hnc* 1| 
the float shmild touch the bottom or a snag in its passage, the ne 
shorter length should be used until the float passes both lines frcel^ 
Floats should be run at frequent intervals across the stream usuaQ 
at each of the tagged stations. 




ream GauglngT 






Extensive experiments were made by Francis at Lowell, Mass., 
tn 1852 to determine the accuracy of rod float measurements.* 

He found that discharge measurements based on the determina- 
tion of velocities by floats were nearly always large as compared 
with measurements by a standard weir. This was due to the fact 
that the rod, on account of not reaching the bottom, was not 
aflfected by the low velocity near the stream bed and hence indi- 
cated too great a velocity. He found that the effect could be cor- 
rected by multiplying the discharge as obtained by the floats by a 
coeflficient as follows: 

(0) Q = CQi in which 

Q = actual discharge 

Qt — discharge as determined by floats. 

C = coefficient = 1 — 0,116 (V^D"— 0.1) and 

_ . distance of bottom of float from bottom of Btream 

D = rat JO — ; — -r — ^- 

depth ot stream. 

It will be obser\'ed that this coefficient C is always less than 
unity except where D is less than 0,01 which condition could not 
be possible in any natural stream. 

The Francis experiments were made in a channel of rectangular 
cross section and floats of uniform length were used* In a natural 
stream the depth will vary at diflferent points in the cross section 
and floats of different lengths must be used. In such cases D will 
vary widely for the various floats used and to apply the correction, 
the velocity as determined by each float should be reduced by its 
particular consatnt, C 

Experiments made at the Cornell Hydraulic Laboratory in 1900 
by Kuichling, WilHams, Murphy and Boright confirmed Francis' 
conclusion that rod float measurements are too large, only two out 
of thirty being smaller than measurements made by a standard 
weir. No attempt was made, however, to verify Francis' formula 
for the correction of such observations.* 

In calculating the discharge from these measurements the ave- 
rage cross-section» in square feet, of each division is calculated and 
multiplied by the average velocity for the same in feet per second 
and the product will represent the discharge in cubic feet per second 
of the section represented by that float and the sum of the sections 
of all the floats will give the total discharge of the stream. 

• See *Txiw^tl Hydraulic Experiments" by James B, Francis, pp. 146-20S. 
*See W. S, & L Paper No, 05» Accuracy of Stream Me els u rem en ts. p- 64. 



K^ 230 


The Meftiurcment o£ Stream Flow. 1 

10 » do 40 DH 60 ;d 6D 90 100 lli 1 


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Area of one square 
equivalent to 2i cu. ft. 
per second* 

Area within discharge 
curve equals 341,6 »q. 
Diecharige: 

2} X 34L6 = 354.1 
OIL ft. per. aec^ 




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;. 13&* — Oraphic Determination of Stream Flow From Measu 

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remanti^ 

J 



The Applicatiocn of Stream Gaugings. 231 

is frequently desirable to calculate the discharge graphically, 
h niay be done as shown by Fig. 125. This is done by plotting 
wo sections at the tag lines over each other and drawing in an 
age section between them. It is frequently desirable to draw 
e floats in their true length and average position so that it may 
;en at onv'e how well the section was covered by the floats, 
ider each float is laid off the velocity as determined by the 
!, to a seltcted scale, and a mean velocity curve is drawn 
lagh these points. By multiplying the ordinate of the velocity 
e by the ordii^atesl of the mean section, a quantity is obtained 
le discharge cmve which, when fully constructed, gives a dis- 
ge polygon, the area of which represents at the correct scale 
discharge in cubic toet per second of the stream. 

0. The Application %A Stream Gaugings. — A single measure- 
t of stream flow is of comparatively little value as a basis for es- 
ting the continuous chaiacter of the flow of the stream, as will 
5tn by examination of any of the hydrographs previously shown, 
flow of a stream, while it niay appear to the casual observer uni- 

1, is actually subject to many and violent fluctuations and the 
may vary several hundred per cent, from minimum to maxi- 

n within a few days. 

has already been pointed out that in order to study the flow of a 
am intelligently it is necessary to know the variations in flow 
: take place from day to day for a long term of years during 
ch the effect of the extreme of all of the factors controlling 
am flow may have made themselves manifest. 
Tic actual measurement of the flow of a stream by current meter 
ioats is usually accomplished with considerable difficulty, and it 
lid be practically impossible to repeat such measurements daily 
the length of time for which records are desired. It has 
tady been pointed out that under many conditions it is possible 
:stablish a discharge or rating curve which will show the relation 
he height of the water surface to the flow through orifices over 
rs or through channels of various forms. In the establishment of 
h relation it is assumed that the raising of the water surface to a 
tn height is always accompanied by the same flow of water 
)ugh the section. In order to assure accuracy in the observa- 
s based on such a rating curve, sections must be selected where 
conditions assumed are correct. Such stations should be se- 
fd, where possible, on a fairly long uniform reach of the stream 





232 The Measurement of Stream Flow* 


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Literature. 233 

and the influences of the back water from large rivers or 

gaugings of the stream have been made under a considerable 
conditions and a rating curve is established therefrom, it is 
ssary thereafter to measure the daily flow but only to note 
5 gauge height. It has been determined by many observa- 
nt under constant conditions a fixed relationship exists be- 
auge height and the discharge of a stream, subject to the 
le to variable flow as described in Chapter X. If the section 
sr conditions of the stream flow remain unchanged, the rat- 
re will remain constant and hence the daily gauge height 
uickly read and recorded and will give at once, by reference 
ating curve or table, the quantity of water flowing in the 
it all times. 

the soundings and levels made to determine the cross sec- 
area curve can be constructed showing the variation of 
:h gauge height. The float or current meter observations 
the necessary data for the construction of a curve of mean 
s. The product of the area and mean velocity, as shown 
i two curves, for any given gauge height, must equal the 
:e and must equal the reading of the discharge curve for 
e gauge height. The construction of these curves, and a 
ation of their properties, furnishes a check on the construc- 
the discharge curve and aids materially in correcting any 
t irregularities therein.* 

26 shows the discharge, mean velocity and area curves for 
)mac River at Point of Rocks, Md. 



LITERATURE. 

8TBEAM GAUGING. . 

igarten, M. Pulsations of Velocity in River Current. Annales des 
Fonts et Chaussees. 1847. 

idy of the Law of Flows in Rivers, Oscillations of Velocity, Obser- 
vations of Vertical and Transverse Velocity Curves. Annales 
des Fonts et Chaussees. 1847. 

, Jas. R. Flow of the West Branch of the Croton River, N. Y. 
Trans. Am. Soc. C. B. vol 3, pp. 76-90. 1874. 

Theo. O. Flow of Water in Open Channels. Trans. Am. Soc. C. B. 
vol. 6, pp. 250-258. 1877. 



River Discbarge," — Hoyt and Grover. 
14 



^34 



The Measurement of Stream Flow. 




5. Wood, de Yolaen, Flow of Water In Rivers. Trans. Am. Soc. C. E. vol. 

8, p. 173, 1879, 

6. McMatb, R. E. River HydraiiHcs. Trans. Am, Soc, C. E, vol 9, pp. Ill 

390. ISSO. 

7. McMatb* R. E. The Mean Velocity of Streams Flowing In Natural CliaB- 

nela. Trans. Am, Soc. C. E. vol. 11, pp. 186-211, 1882. 

8. Current Meter Measurements on the Rhine. Allgeraeine Bauzeltung, Vol 

47, pp. 53-80. 1SS2. 

9. Unwtn, W. C. Current Meter Observations In the Thames. Proc lnH 

a K Vol. 71, p. 33S. 1883. 

10. Stearns, F. P, Why the Maximum Velocity is Below the Surface. Trans 

Am. Soa C. E. Vol 12. p. 331. 18S3. 

11. Cunningham^ Allan. Recent HydrauHc Experiments. Proc. Inst C. E 

Vol. 71, p. 1. 1883. 

12. Fteley, A. and Stearns , E. P. Description of Some Experiments on tN 

Flow of Water. Trans. Am. Soc. C. E. Vol. 12, pp. M18. ml 

13. Measurement of Water. Buh fi, Montana Agric. Expt Sta. 18SS. 

14. Isakoski, R. Discharge of Rivers from tlie Drainage Areas. Zeitscbr*^ 

d Oesterr. Ing. u Arch. Ver. ISSfi, pp. 09*9S. 

15. Seddon, J. A. Consideration of the Relation of Bed to the VariibM 

Jour. Assn. Eng. Soc, Vol 5, p . 127. 18SG. 

16. The Determination of Normal Cross-Sections of the Elbe. TauherL Zalt- 

schrlft fur Bauwesen, pp. 5B1-5C2. 1886. 

17. Green, J. S> Fourth Biennial Report State Eng. of Colo, 1$89. 
IS. Bazln, M. Recent Experiments on the Flow of Waters over Weirs. 

nales des Ponts et Chaussees, Oct. 1888; see also Proc. Ensj. < 
of Phlla. Vol 7 p 2C0. 1890, 

19. Flynn, P. J. Flow of Water in Irrigation Canals. San Francisco. Pubj 

lished by the Author. 1892. 

20. Oangulllet, E. and K utter, W. R. A General Formula for the Ualfon 

Flow of Water in Rivers and Other Channels. Trans, by Herim 
and Trautwine. New York. Wiley H Sons. IS 93. 

21. Foss, W. E. New Formula for Calculating the Flow of Water in Pities ao^ 

Channels. Jour. Asso. Eng. Soc. Vol. 13, p. 295. 18S4. 

22. Flynn and Dyer. The Cippoletti Trapezoidal Weir. Trans. Am. Soc C 

Vol, 3^, p. 9, 1S94, 

23. Carpenter, L. G. Measurement and Division of Water, Bui. 27, Colfl 

Agrlc, Expt. Sta., Fort Collins. Colo. 1894. 

24. Newell. F. H. Discharge Measurements of Streams. Proc. Eng. €l^^ 

Phila. Vol. 12. No. 2, p. 125. 1895. 

25. Humphreys, D. C. Discharge Measurementfl. Jour, Assn. Eng. Socs. ?o( 

IE, No. 5, p. 187. 1805. 

26. Starling, Wm. The Discharge of the Mississippi. Trans. Am, Soc. C. 1 

Nov, 189S. 

27. Grunskj'v C. E. Method for Approximate Gauging of Rivers. Eng. 

March 1, 1890 

28. Keating, W. J. CoeJhclents in Hydraulic Formulas. Jour. Wea. Soc. 

Vol. 1, p. 190. 1896. 

29. Johnson, F. T. and Cooley. E. L. Experimental Data for Flow over Br 

Crest Dam. Jour. Wes. Soc. Eng. Vol. 1, p. 30. 1S96. 



Literature. 



235 



n. 
n. 

34. 
35. 

16. 

tt 

SI 

4S. 
17. 

51. 



A Study of Gauging Statistics. Annates dea Fonts et Cbauaseos. Part IIL 
1897. 

Jasmund, R, Variation In Valoclty In Croaa- Section of a Stream. Efr 
peclally with Obstructions on the Surface and Ice. Zeitschr. fiir 
Bauwesen. 1S9T, pp. 303, 465, 5SS. Centrallb. der Banverwaltung 
p. 101. 

Jobnson, Clarence T. Stream Gaugings. Proe. Purdue Soc. Civ. Eng. 
1897. 

Skinner, Jobn W, Description of the Method of Gauging the Discharge 
Through the Outlet of Hemlock Lake, N. Y. Trans. Assn, Civ. 
Enga* of Cornell University. 1898. 

Blndemann, H* DitTerence Between Average Flow and Flow at Center of 
Stream. Central blatt der Bauverwaltnng, p. 63S. 1S9S, 

Llppincott, J, B. Low Water Measurements in the State of California dur- 
ing the Summer of 1898. Eng. News. Jan, 12. 1899. 

Average Velocity of Water fn Natural Streams. Zeitscbrirt. fflr Gewas- 
ser, pp. 20^36. 1899, 

Newell, F. H. Stream Measuring in the United States. Scl. Am. Sup. 
Nov. 11, 1899. 

Fuchfl, Paul. The Measurement of the Velocity of Flow of Streams. Go- 
Bundbeits Ing. Nov. 30, 1899. 

Sttwart, Clinton B. Discharge Meaaurements of the Niagara River at 
Buffalo. N, Y. Jour, W. Soc. Engs. Dec. 1899. 

tnveetigation of Relationship of Average Flow of a Stream with the Flow 
at the Center, Zettschrlft fur Gewas&er, p. 212. 1900, 

Manaer of Movement of water ia Streams. Zeltschr. fiir Bauwesen. Nos, 
Vn to rX. Centralblatt der BauverwaUung, p. 611, 1900. 

M^tliods of Stream Measurement Water Supply and Irrigation Paper 
No. 56. I90L 

Murphy, E. C, Accuracy of Stream MeasuremenL Water Supply and Irri- 
gation Paper, No. 64. 1901. 

Turneaure and Russell. Public Water Supplies. Chap. 12. New York. 
Wiley & Sons. 190L 

Tutlon, C, H. The Laws of River Flow. Jour. Assn. Kng, Soca. Jan. 
ary, 1902. 

The Natural Normal Sections of Streams, Zeltschr. d Oesterr. Ing. u Arch 
Ver- Feb. 21, 1902. 

Relation of Surface to Mean Velocities of Flow.— An investigation Con- 
ducted by J. B. Lippincott and others in the West. Eng. News. 
Vol, 1, p. 424, 1903. 

Aanua] Report Chief Eng. U. S. A. 1900. Appendix I. L I. Survey of N. 
and N. W, Lakes. Same 1902. Appendix B. E, E. and 1903 Ap- 
pendix F. F. F. 

Presaey, H. A. Methods of Measuring Velocity In River Channels. Sci. Am. 
Sup. Sept, &, 1903. 

Merrlman^ Mansfleld. Treatise on Hydraulics. New York, Wiley & Sons. 
1903. 

Belliiis, E. D. Hydraulics with Tabiea New York. D, Van Nostrand 
Company, 1903. 





236 The Measurement of Stream Flow. 

62. Murphy, E. C, Hoyt, J. C. and Hollister, O. B. Hydrographlc Manual of 
the U. S. G. S. Water Supply St Irrigation Paper No. 94. 1904. 

53. Ho3rt, John C. Methods of Measuring the Flow of Streams. Bng. New& 

Jan. 14. 1904. 

54. Miller, C. H., Pratt, R. W., Rohinson, H. F. Methods of Determining 

the Mean Velocity of Cross-Sections. Eng. News. Vol. 1, pp. 
258-307. 1904. 

55. Anderson, R. H. Some Flood Discharges and Values of "n" in Ratter's 

Formula. Eng. News. Aug. 4, 1904. 

56. Hoyt, John C. Methods of Estimating Stream Flow. Eng. News. Aug. 4, 

1904. 

57. Recent Russian Studies of Flow in Rivers. Eng. News. Sept 1, 1904. 

58. Stout, O. V. P. Notes on Computation of Stream Measurements. En& 

News. Vol. 2, pp. 521-547. 1904. 

59. Mullins, J., and Span, F. N. Irrigation Manual. 1906. 

60. Hermanek, Johann. The Mean Velocity in Natural and Artificial Chan- 

nels. Zeitschr. d Oesterr. Ing. u Arch Ver. Apr. 21, 1905. 
01. Murphy, E. C. A Method of Computing Flood Discharge and Cross-Section 
Area of Streams. Eng. News. Apr. 6, 1905. 

62. Barrows, H. K. Work of the Hydrographlc Branch of the United States 

Ceol. Sur. in N. E. and a Discussion of the Methods used for Es- 
timating Stream Flow. Jour. Assn. Eng. Socs. July, 1905. 

63. Butcher, W. L. The Gaging of Streams hy Chemical Means. Eng. News. 

Dec. 14, 1905. 
C4. Hoyt, J. C. and Grover, N. C. River Discharge. New York. J. Wiley I 
Sons. 1907. 



CHAPTER Xn. 

WATER WHEELS. 

xai. Classification of Water Wheels. — ^Water wheels include 
most of the important hydraulic motors that are adaptable to large 
hydraulic developments. They may be divided into three classes, 
viz: 

First — Gravity wheels. 

Second — Reaction wheels. 

Third — Impulse wheels. 

In gravity wheels the energy of the water is exerted by its weight 
acting through a distance equal to the head. 

In both reaction and impulse wheels the potential energy due to 
the weight of the water under the available head is first converted 
into kinetic energy. This kinetic energy does work in the reaction 
wheel through the reactive pressure of the issuing streams upon 
the movable buckets from which they issue. 

In the impulse wheel the nozzles or guides are stationary and 
the energy of the issuing streams is utilized by the impulsive force 
which they exert in impinging against movable surfaces or buckets. 

Figs. 127, 128 and 129, which illustrate the various types of 
wheels included in the above classes, are adapted, with many mod- 
'fications from Reuleaux's "Constructor." * 

laa. Gravity Wheels. — Fig. 127 shows the various types of gjav- 
^^y water wheels or those wheels that are driven by the weight of 
^he water. At moderate velocity, these motors are practically 
Operated by gravity only, although under some conditions the im- 
pulse due to the velocity of the entering water may have an appreci- 
^'>Ic effect. In Fig. 127, A is an undershot water wheel ; B is a 
"alf-breast wheel (see also Figs. 3 and 4), and C is a high breast 
^heel. D is an overshot wheel. In C and D the buckets should be 
^0 designed as to retain the water until they reach the lowest point 
*n the revolution of the wheel. E in this Figure illustrates Dup- 

•"The Constructor." F. Reuleauz— tnuiB. by H. H. Suplee, Philadelphia, 
'a., 1893. 



338 



Water Wheels. 




af; 



A 








5?^?i^n; 



i^ 








iM^^e^V^ir, 





II 




Fig. 127. — Diagram of Gravity Wheels. 




^Reaction Wheels. 23jf 4 

ngcr's side-fed wheel. F illustrates an endless chain of buckets 
hich is essentially the same in principle as the overshot wheel. G 
a similar arrangement using discs running with as small a clear- 
icc as possible in a vertical tube. When the water acts only by 
avity, the wheels represented by A to E, inclusive, are only prac- 
:able when the wheel can be made as large or larger in diameter 
an the fall of the water. Where small diameters must be used,, 
c arrangements shown in F and G are available. Very small 
heels acting under high pressures may be employed by making 
5C of the so-called chamber wheels, illustrated in H, I and J. 
123. Reaction Wheels. — The wheels illustrated by the diagrams 
I Fig. 128 are of the second class or reaction wheels. Diagram A 
lustrates Barker's Mill of the form known as the Scotch turbine 
lustrated also by Fig. 8. This form of turbine is known in Ger- 
lany as the Segner wheel. The water enters the vertical axis and 
ischarges through the curve arms. B represents a screw turbine 
^hich is entirely filled with water. C shows a Girard current tur- 
bine which has a horizontal axis and is only partially submerged. 
) is Cadiat's turbine with central delivery. It resembles the Four- 
leyron turbine except that there are no guides to direct the flow 
nto the buckets. E is Thompson's turbine with circumferential 
iciivcry and horizontal axis. The discharge from this turbine is 
ibout the axis at both sides. 

In diagrams A, B, C, D and E the column of water is received as a 
•vhole and enters the wheel undivided. The remainder of the forms 
Huslrated in Fig. 128 show wheels in which the flow is divided into 
I number of separate streams by guides interposed in the streams 
Wore the water enters the wheel. Diagram F illustrates the Four- 
ficyron turbine which acts with central delivery. The guide vanes 
ire fixed and the discharge of the water is at the circumference of 
^He wheel. The ordinary vertical form of the Fourneyron turbine is 
fetrated in Fig. 128. Diagram G, also in Fig. 128, is a modification 
^f the Fourneyron turbine in which the water is being delivered 
^pvi-ard from below. This form is sometimes called the Nagel's tur- 
bine. Diagram H is the Jonval or Henschel turbine. (See also 
^?- '35') The guide vanes in this turbine are above the wheel 
^hich is entirely filled by the water column. Diagram J is the 
'rancis turbine in practically its original form. (See also Fig. 14.) 
diagram I illustrates the present American form or modification of 
le original Francis turbine. K is the Schiele turbine, a double 
leel with circumferential delivery and axially directed discharge. 



2^0 



Water Wheels. 















Sis* 128.— Diagrams of ReacUoa Wheell. 



L 



Itnpiilse Wheels, 2^1 

In forms H, I, J and K, a draft tube may be used below the wheel to 
utilize any portion of the fall which occurs below the level of the 
bottom of the wheel. 

In all reaction turbines, the water acts simultaneously through a 
number of passagfes around the entire circumference of the wheel. 
In the impulse or action turbine, the water may be applied to all of 
the buckets simultaneously or to only a portion of the circumference 
at a time, 

134, Impulse Wheels, — The wheels illustrated in Fig. 129 are the 
third class of wheels which are driven by the impulse due to the 
weight of water acting through its velocity. Of these wheels, A is 
the current wheel or common paddle wheel. The paddles are 
straight and either radial or slightly inclined toward the current, 
as in the illustration. (See also Figs, i and 2,) 

Diagram B is Poncelet's wheeL (See also Fig, 5,) The buckets 
run in a grooved channel and are so curved that the water drives 
upward and then falls downward, thus giving a better contacL 

Diagram C shows an externally driven tangent wheel. The buck- 
ets are similar to- the Poncelet wheel but with a sharper curve 
inward. The discharge of the water is inward, D is an internally 
driven tangent wheel similar to the preceding but with an outward 
discharge. 

E is the so-called hurdy-gurdy or tangential wheel. The water 
is delivered through a nozzle and the wheel is practically an ex- 
ternally driven tangent wheel of larger diameter and with a smaller 
number of buckets. 

Diagrams F, G and H illustrate three types of impulse wheels 
with inclined delivery. (See also Figs, 6, 7. 9 and 10.) Diagram F 
shows a crude form of vertical wheel similar in form to the Indian 
wheel, Fig, 6. It is used on rapid mountain streams and is probably 
the original conception from which the turbine has been developed. 
Diagram G is the Borda turbine and consists of a series of spiral 
buckets in a barrel-shaped vessel Diagram H is a Danaide turbine 
which has spiral buckets enclosed in a conical tube. This is an old 
form of wheel formerly used in France. 

125* Use oi Water Wheels. — Almost all water wheels in prac- 
tical use are modifications of some of the above forms and by a 
study of these forms a wheel may be classified and a clearer under- 
standing obtained of the principles of its operation. Many of the 
^orms of wheels shown in Figs, 127, 128 and 129 are practically db- 

^lete or are used only in minor plants or for special conditions 





24a 



Water Wheels. 








%.^ 



B 




H 



Fig. 129.— Diagrams of Impulse Wheels 



Use of Water Wheels. 



243 



tat make them of only general interest in the study of water 
power. 

While gravity wheels are still occasionally used their application 
is entirely to the smaller water power plants. In many cases the 
turbines purchased for such installations are of cheaper make, 
Poorly designed, constructed and selected, and often improperly set 
itid, consequently, inefficient. In such cases, and where the ques- 
ion of back water and the interference of ice is not important, the 




ISO.— **OrerrBhot'* Water Wlie#L Manufactured by Fitz Water Wheel Co, 



^vity wheel may be more efficient and quite satisfactory. Well 
%ned and well constructed gravity wheels are said to give effi- 
Dcies of 85 per cent, and above, (See Frontispiece and Fig. 
). With such plants the engineer has usually little to do and 
sequently they will not be further considered here. The types 

[wheels now mc^t largely used for moderate and large water 
rer developments are the reaction and impulse turbines. 

Classification of Turbines. — All moder turbines consist of 

vheel ID which buckets are attached and whicn is arranged to re- 
yvrii in a fixed case having attached to it a nozzle, guide 




244 



Water Wheels. 



series of guides. The guide passages or nozzles direct the waicr 
at a suitable angle onto the buckets of the wheel. The revolving 
wheel contains curved buckets or passages whose functions art to 
receive the water, utilize its energy and discharge or waste it u 
nearly devoid of energy as possible. 

Turbines may be classified in various ways; 

First. — In accordance with the action of the water on the same. 

(A) Reaction or pressure turbines^ such as the Fourneyron, Jm- 
valp Francis, etc< (See Fig. 128, G, H, I and J.) 

(B) AcHon or impulse turbines, such as the Girard and tangen- 
tial wheels* (Sec Fig. 129, diagrams D and E.) 

(C) Limit turbines, which may act either by reaction or impulst 
Second.^In accordance with the direction of flow in reference 

to the wheeK 

(A) Radial fiotv turbines. In these turbines the water flows 
through the wheel in a radial direction, Tliese may be subdivided 
into — 

(a) Outward radial flozv turbincSf such as the Fourneyron and 
Cadiat. ,(See Fig. 128, diagrams F and D,) 

(b) Inward radial ftouf turbines, or wheels in which the water 
flows inward in a radial direction such as the Francis and Schtlk 
turbines. (See Fig. 128, J and K.) 

(B) Axial flow turbines in which the general direction of the 
water is parallel to the axis of the wheel such as the Jonval and 
Girard wheels of similar design. (See Fig. 128, H») 

(C) Mixed flow turbines, or turbines in which the flow is 
tially radial and partially axial as in turbines of the American 
(See Fig. 128, diagram I; also Figs, 143 to 15S inclusive). 

Third. — In accordance with the position of the wheel shaft 
(A) VerHcal (See Figs. 132, 134, 135, 151, etc.). 
fB) Horizontal (See Figs, 140, 152,) 

Fourth, — In accordance with the arrangement of nozzles 
guides, 

(A) Complete ti4rbines with guides surrounding the entire whi 

(B) Partial turbines with guides partially surrounding the wh< 
in one or more groups. 

The re-action turbine is a turbine with restricted discharge whii 
acts through the reactive pressure of the water. Under some con* 
ditions the energy of the water may be exerted, at least in pat 
by its impact or momentum. The impulse turbine acts prindj 



I 



Condition of Operatioti. 245 

^ly through the momentum of the moving mass of water although, 
when the current reverses, some reactive pressure may be recog- 
nized. The limit turbine may act entirely as a reaction or as an 
impulse turbine according to the conditions under which it oper- 
ates. 

127. Condition of Operation. — These wheels operate under the fol- 
lowing conditions : 

REACTION OB PRESSURE TURBINES. 

Guides complete. 
Buckets with restricted outlets. 
Buckets or wheel passages completely filled. 
Energy most largely developed through reactive pressure. 
Discharge usually below tail water or into a draft tube. 

ACTION OR IMPULSE TURBINES. 

Guides partial or complete. 
Buckets with outlets free and unrestricted. 
Wheel passage never filled. 
Energy entirely due to velocity. 
Discharge must be above tail water. 

No draft tube possible, except with special arrangement which 
will prevent contact of tail water with wheels. 

UMIT TURBINES. 

(A) Buckets so designed that the discharge is unrestricted when 
above tail water. 

Buckets in this case are just filled. Act without reactive effect. 
Discharge above tail water. 

(B) If tail water rises to buckets, the discharge is restricted and 
reaction results. 

In this case the full bucket admits reaction and discharge may be 
Wow tail water. 

19& Relative Advantage of Reaction and Impulse Turbines. — 

jfihe reaction wheel is better adapted for low and moderate heads, 

especially when the height of the tail water varies and where the 

amplitude of such variation is a considerable percentage of the 

fetal bead. Such a wheel, which is designed to operate with the 

dockets filled, can be set low enough to utilize the entire head at 



246 



Water Wheels* 



all tim^s and will operate efficiently, when fully submerged, 
reaction wheel can therefore be set to utilize the full head at tin 
of low tail water and when the quantity of flow is limited. ¥a 
low head developments this is an important factor. The impiilK 
turbine, on the other hand, must have a free discharge and mu 
therefore be set far enoug^h above the tail water to be free from bad 
water if it is to be operated at such times. 

Another difference between the reaction and the impulse turbin 
is the higher speed with which the former operates. This is olta 
a distinct advantage, for direct connection with high speed 
chinery, and with low and moderate heads. On the other han^ 
with high heads the slower speed of the impulse wheels is frequentljj 
of great advantage, especially in the form of the tangential whff 
when the diameter can be greatly increased and very high head 
utilized with moderate revolutions. In such cases the height ■ 
the back water is usually but a small percentage of the total he 
and the loss due to the higher position of the wheel is compaci 
tively small. 

The speed of a wheel foe efficient service is a function of the ratwlj 
of the peripheral velocity of the wheel to the spouting velocity ( 
water under the working head. This ratio will vary from ,65 to . 
in reaction turbines, according to the design of the wheel. In in 
pulse' turbines this ratio varies from .40 to ,50. 

129. Relative Turbine Efficiencies. — ^The impulse turbine has the^ 
further advantage of greater efficiency under part gate, — that is* 
at less than its full capacity. When, as is usually the case, a wheel 
must operate under a variable load it becomes necessary to rcduo 
the discharge of the wheel in order to maintain a constant sp 
with the reduced power required. (See Fig. 131). This is le 
compHshed by a reduction in the gate opening which commonly 
greatly aflfects the economy of operation. 

The comparative efficiencies of various types of the turbines i 
shown in Fig, 131. The maximum efficiency of turbines whc 
operated at the most satisfactory speed and gate will be about th 
same for every type, if the wheel is properly designed and coa 
structed and the conditions of operation are suitable for the typ 
used. This maximum efficiency may vary from 75 to 85 per cent 
or even between wider limits, but, with suitable conditions^ shouJfi 
not be less than 80 per cent. In order to make the curves on thq 
diagram trnly comparative, the percentage of maximum efficient 



Relative Turbine EflSciencies. 



247 



10 



20 



— - — \^-'^ :ss 


^ ^ ^''=H ^5^ ^ 


J^ ^ Z ^'^ 


^'^ ^ -^ J^ ■ 


7 ^'^ f \y 


^ / 4 ./ ■ 


ft zw -.fizw ■ 


^l ii ^twi 


-€ ^/_ _±/2: _j 


jp // f/lW ■ 


h 1 i. tt 


t ' -IT • 


-A t 4 21 


-/ t J/- ' 


4- - -f 


1- X ^ Zj 


ti t J 


. t ' '^^ 


x/ 77: 


: JZl J2 



30 40 SO 60 70 

PER CCNT or MAXIMUM OISCHARGC 



80 



90 



100 



Fig. 131. — Comparative Efficiencies of Various Types of Turbines. 

A of maximum discharge are plotted instead of the actual efli- 

mcies and actual discharge. 

The Foumeyron turbine usually shows very poor efficiencies at 

rt gate as shown in Fig. 131. The curve for this turbine is 

iwn from Francis* test of the Tremont (Fourneyron) turbine 

5C Fig. 132, also Table LXI) and is substantiated by efficiency 

rves shown by various tests by James Emerson.* 

rhc Jonval turbines usually show better part gate efficiencies 

m the Foumeyron but are not as efficient, under such conditions, 

turbines of the inward flow or Francis type. The Jonval curve, 

>wn in Fig. 131, is plotted from the test made in 1884 at the 



See "HydrodTnamics" by James Emerson. 



^49 



Water Wheels. 



L 



Holyoke testing flume * of a 30-inch regular Chase- Jon val turbine, ' 
(See Table LXXVl), 

The American-Francis turbine varies greatly in part gale effi- 
ciency according to the details oi design and the relation of speed 
and head under which it operates. The curve shown in Fig, IJU 
representing this type, is from the test of a wheel manufactured by 
J* & W* Jolly of Holyoke, Massachusetts, similar but not tlie sara 
as that illustrated by the characteristic curve Fig, 249. 

The impulse wheels when properly designed and operated s]ioi( 
a higher part gate efficiency than any other type of wheel, 
curve shown in Fig, 131 is from a test oi a 12" Doble tangentij 
wheel in the laboratory of the University of Wisconsin.t 

As already indicated, the design of the wheel has a great uj 
fluence on its efficiency at part gate* Individual wheels or 
of wheels of any type may therefore depart widely from the cur 
above shown, which are intended only to show as fairly as possib 
the usual results obtained from well made wheels of each type. 

It should be noted also that efficiency is only one of the facto 
influencing the choice of a wheel and that many other factors mil 
be weighed and carefully considered before a type of wheel is 1 
lected as the best for any particular set of conditions, 

130, Turbine Development in the United States, — ^The dcvtio 
ment of the turbine in the United States has been the outgrois 
of some seventy years of practical experience. In the early setti 
ment of the country the great hydraulic resources afforded faci^ 
ties for cheap power and numerous water powers were develop 
under low and moderate heads. These developments created I 
corresponding great demand for water wheels and stimulated il 
vention and manufacturing in this line, "American inventors bail 
devised many different forms of wheels which were patented, co 
structed, tested and improved to meet the prevailing conditio 
When a successful wheed was designed, it was duplicated in 
original form and its proportions increased or diminished, to co 
form to the desired capacity* As wheels of greater capacity or I 
higher speed have been required, modifications have been mn^ 
and improved systems have resulted. 



* See page 44 of 1S97 catalogue of Chase Ttirbine ManufactarliiS 
Orangcv Mass. 

tFrom "Feftt of a 12* Dohle Tanfrential Water Wheel," an Dnpubliflli 
thesis hy H. J, Hunt and F. M. Johnson* 



^^V Turbine Development in the United States. 2^9 

The best American water wheel construction began with the 
Boyden-Foumeyron and Geylin-Jonval turbines of improved 
French desigi^, but modern American practice began to assume its 
characteristic development with the construction of the Howd- Fran- 
cis turbines, already described* Moderate changes in the form and 
arrangement of buckets and other details gave rise to the earlier 
forms of "Swain," "LefFel" and ''American" wheels each of which 
consisted of an inward flow turbine modified from the earlier de- 
signs of Hawd and of Francis as the experience of the inventor 
seemed to warrant. In all of these cases the wheels discharged 
inward and essentially in a radial direction and had to be built of 
sufficient diameter to provide an ample space for receiving the dis- 
charging waters. This necessitated slow speed wheels of com- 
paratively low capacity (see Table I, page 13), In order to secure 
higher speed, the diameters of the wheels were reduced thus re- 
ducing the power. This reduction was, however, more than coun- 
terbalanced, in the later wheels, by an increase in the width of 
the bucket in an axial direction. It was found also that the cap- 
acity of the wheels could also be materially increased, with only 
small losses in efficiency, by decreasing the number of buckets- 
Wheels were gradually reduced in diameter and the buckets in- 
creased In breadth until, in many cases, they reached very nearly 
to the center of the wheel This necessitated a downward dis- 
charge in the turbine and resulted in the prolongation of the buck- 
ets in an axial direction in many cases to almost double the width 
of the gate. From this development has resulted the construction 
of a series of wheels known as the "American turbines*' having 
bigher speed and greater power than has been reached in Euro- 
pean practice. 

The entire line of development has, until within the last fifteen 
years, been toward the increase of speed and power for low and 
moderate head conditions. It is only within this period that a con- 
si<3erable demand has been felt in this country for tuitiines having 
other characteristics and adapted for higher heads. 
■The American type of turbinei in its modern form is not designed 
or suitable for high heads its origin being the result of entirely 
different conditions. About 1890 came a demand for turbine wheels 
under comparatively high heads which manufacturers of wheels of 
the American type were therefore poorly equipped to meet The 
^rst of such wheels supplied were therefore of European types, 



n 




2 50 



Water Wheels. 



which apparently better suited such conditions, Recogoizing, 
however, the importance of meeting such demands^ the Amerian 
manufacturer found that the wheels of essentially the origiiial 
Francis type were well suited for this purpose. The narrow wheel 
and nuraerous buckets of the earlier types rednced the discharge of 
water, and, increasing the diameter, reduced the number of revo- 
lutions. Such t^pes of wheels of high efficiency can now be 
obtained from the leading manufacturers in the United States, aod, 
while many manufacturers still prefer to furnish simply their stock 
designs, which are only suited for the particular conditions for which 
they were designed, still, other manufacturers are prepared to 
furnish special wheels which are designed and built for the particu- 
lar conditions under which they are to be used. 

The systems of wheels offered by American manufacturers, which 
can be readily and quickly duplicated at a much less expense than 
would result from the design of special wheels for each particular 
customer, has resulted in the ability of American manufacturers to 
furnish water wheels of a fairly satisfactory grade and at a cost 
which would have been possible in no other way. In the United 
States the cost of labor has been comparatively high and special 
work is particularly expensive, much more so than in Europe where 
skilled mechanics receive a compensation for labor which is but 
a small fraction of that of their American cO(m pet iters. Average 
American practice, at the present time^ leaves undoubtedly mticHj 
to be desired and considerable advance may be expected from the I 
correction of designs, resulting from practical experience and by ti^t j 
application of scientific analysis, 

131. The American Foumeyron Turbine. — As noted in Chapterl 
I, one of the first reacticai turbines developed in the United States J 
was the Boyden wheel of the Fourneyron type. 

In these wheels (see Fig. 132) the water entered from the Genter|| 
guided by fixed curve guides, g, (Fig. 133) and discharged outward 
through the buckets^ B. The use of these wheels gradually spread 
and they rapidly replaced many of the old overshot and breasl 
wheels used up to that time, and soon became the foremost whe 
in New England- 

The manufacture of the Fourneyron turbine has, for commo 
use, been discontinued on account of the competition of olhe 
cheaper wheels which were fooind to be more efficient at pan gat( 



k 



252 



Water Wheels. 



and more generally satisfactory under ordinary conditions of sm- 
ice. 

The Fonrneyron turbine, when well designed and constructed, i^ 
a turbine of high full gate efficiency. This wheel is adapted for 
high heads where a comparatively slow speed is desired, — and u 
is now frequently used for high grade and special work where its 
peculiarities seem best suited to such conditions. ' 

One of the modern applications of the Fourncyron turbint \^ 
that in the power plant of The Niagara Falls Water Power Com- 
pany< Fig* 134 shows vertical and horzontal sections of one of the 
double FournejTon units used by this company in their first plant 
These wheels discharge 430 cubic feet per second and make 2^ 
revolutions per minute; at 75 per cent* efficiency each wheel wili 
develc^ S^ooo horse power. The buckets of these wheels are di- 
vided vertically into three sections or stories in order to increase 
their part gate efficiencies. These wheels are of Swiss dtsign by 
the firm of Faesch and Picard and were built by The L R Morris 
Company of Philadelphia. (The wheels are vertical and connecte^t 
by vertical shafts, each with one of the dynamos in the staiioii 
above. The shaft is built of three-quarter inch steel, rolled into 
tubes 38 inches in diameter. At intervals the shafts pass through 
journal bearings, or guides, at which points the shafts are reduced 
to II inches in diameter and are solid* The speed gates of these 
wheels are plain cytindrical rims which throttle the discharges 
on the outside of the wheels and which, with the co-operation of 
the governor, keeps the speed constant within two per cent under 
ordinary conditions of operation. Another wheel of this type is 
that manufactured and installed at Trenton, Falls, N. Y„ by 1^"*^ 
same firm> (See Fig. 51 1») 

132, The American Jonval Turbine.— The Jonval turbine, orig- 
inally of French design, was introduced into this country about 
1850 and became one of the most important forms of turbine of 
early American manufacture. In the tests of turbines at PhiU^ 
delphia in 1859-60 (see page 360) a Jonval turbine developed th^ 
highest efficiency and the type was adopted by the city for use iJ> 
the Fairmount Pumping Station, Like the Fourneyron turbinc« 
these wheels, while highly efficient at full gate, have largely hcco 
superceded by other cheaper and more efhcient part gate types*-^ 
except for special condition s. 




I 



The American jonval Turbine. 



253 




134.— Doutle Fmirnejrron Turbfiie of The Niagara Fa\W ^aUt Tc^^^t 
npaay. { Designed by Faesch & PIcard; built by L P. Mor ^>^A 



^54 



Water Wheels. 



Fig- 135 shows the Geylin-Jonval turbine as manufactured bv- 
the R. D, Wood Company of Philadelphia, W represents the mn- 
ner, B the buckets which receive the water throug^h the guides, |, 
The wheel shown has double inlets that are closed by the douWe 

cylinder gates, GG, This 
gate closes op against the 
hood, C» by means of the 
rod r. r, which connect 
with the governor mech- 
anism. The general de- 
sign of the ordinary whctl 
of this type is perhaps 
best shown by Fig. 136.* 
In this figure A is the 
fixed or guide wheel and 
B is the movable or tur- 
bine runnen 

In the later hydraulic 
developments the use o( 
this wheel has been con- 
fined, largely at least, 
to locations that require 
special designs. Ooe 
of the Later develop- 
ments of the Jonval tur- 
bine has been that for 
The Niagara Falls Paper 
Company, The first in- 
stallation consisted of three upward discharge Jonval turbines of^ 
1,100 horse power each, under a head of 140 feet The installatioii 
provided, however, for a total installation of six turbines. The ver- 
tical shafts are 10 inches in diameter and 140 feet in length atid 
weigh about 19 tons each. These shafts, in addition to the weighf 
of the wheels, — which are 4' 8" in diameter, arc supported by marine 
thrust bearings, under the beveled wheels, together with a step^ 
bearing under the turbine. When the turbine is in use, however; ^ 
the weight of the wheel and the shaft is balanced by the upward 
pressure of the water which at two-thirds gate is designed to ex- 
actly balance this weight. At fo^ill gate there is an unbalanced up* 




Fig. 135.— Vertical Gey] In- Jonval Turbine 
(Manufactured by R, D, Wood & Co.). 



* Sa« page 7, 1877 catalogue, J. L. & S. B. Dlx» Qlen Falls, N. T 




American Jonval Turbine. 



^55 



fpfessurc, and, at less than twothirds gate» an unbalanced 
fcrard pressure; these pressures are, however, only the differ- 
between the weights and the water pressure and are easily 
for by the bearings above described. 

These wheels have thirty open- 

rl ings and operate at 260 revolu- 

I tions per minute. The gates are 

I provided with sleeves (cylinder 

I gates) each weighing 2,800 pounds 

i and slide outside the guide wheels 

to the hood. These sleeves are 
guided by four rods which extend 
above the turbine casing about 10 
feet to a yoke which is ctjunter- 
balanccd. A sectional view of 
one of these turbines is shown in 
Fig, 137 and the general arrange- 
ment of the plant is shown in Fig. 
138. 

A still more recent type of the 
Jonval turbine is the double, hor- 
izontal wheel built for The Niag- 
ara Falls Hydraulic Power and 
Manufacturing Company and in- 
stalled in 1898, (See Figs. 139, 
These wheels have a common, central intake and quarter- 
draft tube which turns down to and is sealed in the tail 
flow the floor. The speed control is effected by a register 
irough which the water passes before it reaches the guide 
!This is said to give a somewhat Io\ver emciency at part gate 
pes a gate interposed between the guide tubes and rimrier 

Economy of water at part gate is said to be no PJ^ i 
tn this plant and reduced efficiency is, in fa.ct, an g 

.^ , . J ^ -^c -a velocity in the 

I it reduces the gate movement and retains <* i ^ 

ck, with a given change of load, and consequently recliiccn 
.» -I f , , ^r^n This turbine U 

atia action and aids the speed regulation. 

tr 1-1 1 .- -^,,+#* under the normal 

2,500 H, R at 250 revolutions per mmute, w 

210 feet.* 




.^JonvaJ TtirMne as Manu 
lired by J. L. & S. B. DU, 



>Tle EleetrJc&l World/* January 14. 1899. 



256 



Water Wheels. 



I 




Fig, 137. — Geylin-Jon%^a! Tarhine of Nia^ura Falls Paper Mill Co. Mintifs^ 
tiired by R. D. Wood & Co. (Frcim Eng, News, Apr. 6. 1S&4.) 

133. The American Type of Reaction Turbine* — The Howd 
Wheel (Fig. 13) from which the idea of the Francis inward flo^^' 
wheel (Fig. 12) was derived, was invented in 1838 and acquired s 
considerable market throughout New England, From these wheels 
originated the American inward and downward or mixed flow Mr- 
bines. 

The early wheels of American manufacture were designed vc^v 
much after the style of the Francis wheel with changes, more of 
less radical, in the shape and details of the buckets. The de^iand 
for wheels of greater power, and higher speed, has resuhed in * 
gradual development of other and quite different forms* 

The development of the turbine in the United States is wrll 
illustrated by that of the *' American" turbine of Stout, Mills k 
Temple, now The Dayton Globe Iron Works Co, This wheel wa& 



i 



L 



J 




American Jonval Turbine- 




^h. 13S, -Plant of the Niagara Fali> 
rkpi*r Co. 8howinf Installatiafi of 
*fcmval Ttirbinep. (From Ca&eier'e 
Magaxine* Nov.^ 1004, 



designed in 1S59 and was called 
I he American Tarbine. The 
f;eneral form of the original tur- 
bine wheel is shown in Fig, 14K 

This was followed (1884) by 
the design of what is known as 
the **New American" turbine, 
illustrated by Fig. 142, In this 
wheel the buckets arc length- 
ened downward and have a 
partially downward as well as 
inward discharge. 

This wheel was foltowed in 
1900 by the **Special New 
American" illustrated in Fig. 
143, having a great increase in 
capacity and power. 

The fourth and most recent 
type (1903) is the "Improved 
New American*' illustrated in 
Fig. 144. The comparative 
power and speed of these vari- 
ous wheels is shown in the 
tables on pages 258 and 259, 

Table XXIII is misleading to 
the extent that while the diam- 
eter of each wheel is given as 
4S" such diameters are not 
strictly comparative. Part of 
the additional capacity and 
power of the * 'Special New 
American" and of the **Im- 
proved New American" is due 
to the cutting back of the buck- 
ets (see Figs, 141 to 144) which, 
while it reduces the diameter 
at the point of nneasurement, 
gives a discharge which would 
be fairly comparative with 
wheels of the older type of per- 
haps three or four inches larger 
diameters. (See Sec, 140.) 



4 
I 



i 



258 



Water Wheels. 



TABLE XXin 

Deveiopmmit of Mm«Hea«* Turbines,— C^padiy^ Spetsi and Fmi^er of a 4I1VA 
Turbine und^r a IS^foot Head* 



Year 
brout^ht out, 



in CM. ft. 



Americftii « 

Standard New American 
New American .,*--**-< 
Special New Amen can >. 
Improved New American 



1859 
lgS4 

1894 
1900 
1903 



3271 

5S64 

9679 

11061 



Rev, per 

(nin. 



102 
102 
107 
107 
139 







m 

141J 



i 



Fiff. 139.— HorlEantal Geylin-JonTal Turtilne of Nta^ara Falla Hydraull^^ 
Power h ManufacltirjQg Ce. Sbowlng Guide Chutes.* 




* Cuts 139 and 140 reproduced from Electrical World, Jan. 14, 1899. Ta^| 
bluea manufactured hy R D. Wood & Co. 



The American Type of ReactioD Turbine, 



259 



The development of turbines may also be illustrated by a compar- 
ison of the size and speed of turbines of various series required to 
develop essentially the same powen {See Table XXIV.) 

|| TABLE XXrV 

Intr€(i»e in Speed of **Am€TiGan" Turbines for Same Poumr (le-foot head). 




New Amerii^n .„♦,...., 
Special New American . , , 
Improved New Amerioin 



Sisteof 
wheel. 



Horse 
power. 



48 
25 



79.1 
81.5 

87.5 



R. P. M- 



102 
136 
186 
267 



I 




Fig. 140— Honzoutal GeyUn— Jonval Turbine .Showing Bucket Ring.* 



Figs. 145 and 146 show a vertical and a horizontal half plan, half 
section of a vertical Improved Kew American turbine, W is the 
crown and hub of the wheel ; B^ the buckets ; G, G, are the wicket 



•See foot note page 258. 




36o 



Water Wheels. 



gates that control the admission of water to the wheels and which 
are operated by means of the ring Gr, which is moved by an ecci^n- 
trie and rod, r, connected with the governor throoigh the shaft, P. 

The inner edges of the bucket are spaced some distance from the 
shaft and the main discharge is inward and downward, though a 
portion of the bucket will admit of a slightly outward discharge. 

134. The Double Leffel Turbine,^ — Perhaps the greatest depar- 
ture of American inventors from the lines of the original Francis 





Fig, 142.— New American 



Fig. 141,— American Turblae Rua- 
nen* 

TABLE XXy, 

Ikvelopment of "I^Jfef Wheel— Capacity, F&vme' and Bp^d &f 404n4h 

Wheel U-nder IG-foot Mmd> 



i 



Year 

brought out. 



StandBrd , » . , . 

Sfwciftl , , * , w * . . . . 
Samson 

Cmproved Samson. 



1860 
187C 

laeo 

1897 



DUcharge, 



2547 
3Q72 



i 



E«T. per 




• Maiiiifactured by The Dayton Globe Inm Wi>rkB C«l 




The Acncrican Type o£ Reacuoa Wheels, 263 




flm. 147 and 148*— SeiJtJon and Plan of Sainaon Turbine,^ 
lufactQrBd ^r The James LelTol k Co. 




j^ 



^02 



Water Wheels. 




^ mm 



flgi. 145 and 146.— Se<!tIoti and Plan of rmprovedNew American Turb 



♦Manufflcturea by The Dayton Globe Iron Works Co, 




The American Type at Reacuoa Wheels, 363 




Pigi. 147 and 148.— Section and Plan of Samson TurblneL* 
lolftctnred by Tbe J&m«fl Lelfel A Co. 




264 



Water Wheels, 





Figs. I49p 150 and 151, — Top View, Runner and OuUlda Ttew of Saaj^n ' 

bine.* 



* Manufactured by Tbe James LefTel & COh 




he Double Leffel Turbine* 



«^ater iQward and discharge it downward, outward and inward with 
the general purpose of distributing it over the cross-section of the 
turbine tube. The gates, G, are of the wicket type and are con- 
nected by rods with an eccentric circle which is operated through 
the arm, A, and the gearing, Gr, by the governor shaft, P* The 
gate gearing is well shown by reference to the section-plan^ Fig. 

148, and the top view, Fig. 149. 

The Samson turbine runner is illustrated in Fig, 150, and Fig. 

151 shows an outside view of one of the vertical, turbine units. 




^C 1&£.— Double Horizontal Leffel TurblEe of Tb« Niagara F&lls Hydraulic 
Poww A Manulacturing Co. Manulactured hf Tk© Jamefi L^Sel A Ca. 

^c development of this wheel is illustrated by Table XXV. This 
^l>le Is fairly representative of the growth of this turbine as the 
ujatnetcr is, in all cases, the maximum diameter of the wheeL (See 
^<^. 140.) 

"Hie adaptability of the earlier turbine designs to the later mod- 
^^te head developments is well illustrated in the design of the 




266 



Water Wheels, 



wheels for The Niagara Falls Hydraulic Power and Matiufacttmnff 
Company, installed by The James Leffel Company about 1891 
These turbines have the single naj-rower buckets, smaller discharge 
and relatively slower speed of the earlier designs. The runners arc 
double discharge, horizontal, seventy-four inches in diameter and 1 
operate at a speed of 250 revolutions per minute under a head ot | 
215 feetj and each wheel develops about 3,500 horse power. 




Fig, 153.— Leffel Doubl© Runner of Tbe Niagara Falls Hydraulic Powtbt 
Manufacturing Go. Manufaetured by Tbe James Leffel & Co. 

Fig. 152 shows one of these units complete. Fig* 153 is a vicwj 
of the runner. For a test of this wheel, made December 190J, 
page 381, 

135. Other American Wheels. — The development of moden 
American wheels could, perhaps, have been equally well illustraie 
by the growth of various other American turbines. The deveic 
ment of all American wheels up to the present time has been 
the line of increasing both the speed and the power of the whe 
for low head, with a return to the earlier type for wheels to be ^ 
under the moderate heads- 
Fig. 154 illustrates a runner of the well-known McConnick 
tern, Mr. J. B. McCormtck, who had previously become famiU 



1 



Other American Wheels. 



267 




Tertaiii wheels of large capacity desi^^ned and patented by 
£W and John Obenchain, re-dcsigiied and improved these 
I, about J876, and secured high efficiencies together with 
ltd power far beyond any other wheels of that period. Mc- 

Cormick wheels in their 
original or modified form 
are now made by a large 
number of American man- 
uiacturers and these 
wheels have had a marked 
effect on the design of 
almost 'all modern Ameri- 
can water wheels. The 
runner in the illustration 
is the Hunt-McCormick 
ru n n e r as m an u f ac t u red by 
The Rodney Hunt Ma* 
chine Company, but is 
very similar to the Mc- 
Cormick wheels of various 
other manufacturers. 

The Smith*McCormick 
runner is manufactured by 
The S. Morgan Smith 
Company. This company 
has also recently brought 
out a new wheel called 
the "Smith Turbine/' 
of greater power and 
higher speed, the runner 
of which is illustrated by 
Fig. 155. Fig. 156 repre- 
sents the Victor runner or 
**type A** runner of The 
Piatt Iron Works Com- 
pany, designed for low 
heads, 

Fig. 157 is the "type B" 

runner, of the same Com- 

1S6.— Smith aiinner of S. Morgan pany, designed for medi- 

Smith Co. um heads. This runner 



154. — Htiiit*Mt5Goniil€k Rnnner of The 
Rodnef HuDt Machine Go. 





i 



V 263 ^IV Wilier 


^m^^iH 


^M again illustrates the tendency tc 


) return to the earlier forras i>f| 


^M runner for medium head wheels. 


This 


latter type has also been H 


^m adopted by other manufacturers of turbines, as may be seen by rtl-| 


^H erence to Fig, 158 which shows * 


"'" Hunt runner manufactured for^ 


^^^^ moderate heads by The Rodney Hun' Machine Company. | 


i^^B_ ^^^^^^^^h^ 




Fig. 159 is from a shop 


^^^^_ ^^^^^^^^^^^ 




photograph of the Sbawic^ 


^^^^^B ^^Bm^T Y ^^^B 


k 


igan FaUs turbine raauu' 


^^^^^B ^fW^^^^^L : ^ 


k 


factured by the I, P. Mor^ 


^^^^^ ^^^'-'^■^^Q^fe^^.' 


1 


ri 5 Co m pa ny , Th is is on t 


^^m ^^^^K_ 


i 


of the largest turbines evci 
constructed and develops 
10,500 horse power under 
a head of 140 feet Itiia 
double mixed inflow type 


^^m ^^^^^^^^L^ 


n 


with spiral casing and i 
double draft tube through j 


1 ^^^^^E/' 


A 


which the water discharge ] 


^m ^R,,iHW^"^ 


f 


outward from the center 
The diameter of the cas- 


^^^ ^^^nl^w^ 


1 


ing at the intake is IQi i 


^^ Fig* 156* — Victor or '*Tjpe A" Runner cf 


feet and the sectional 


Tbe Piatt Iron Works Co, 




area gradually dimimshci , 
around the wheel in pro- 
portion to the amount of 
water flowing at each 


^^f^l 


k 


point The wheel com* 
plete is 30 feet in beighi 
and w*eighs 182 tons. The 


^^^!^^^|£^N1K^^^^ 


■ 


runner, which isofbronic, 


^ 


is shown in Fig. 160. A 


Ei^iiflvjfei 


^1 


Figs. 161 and 162 sh0ifl 


li^^^yK 




two sections of a sinfl^^ 
turbine of the Francis il^| 


\^^^^^^^^HH^ 




flow type built for tll^| 
S n oqual mie- Falls plant (mH 


^^Crr^^P^V^B X» 


W 


The Seattle & Tacom« 


"^ A^ LV 




Power Company by TteB 




Piatt Iron Works Com 1 


ng. 15T,— nigh Head or "lype B" 1 


Runner 


pany. The turbine has J 


of The Piatt Iron Works Co. 

L^ 




capacity of about 9.O0fl 



Other American Wheels, 



269 



der 270-foot head st 300 R. P. M, The mnner is 66 inches 
:ter and has a width of 9i inches through the buckets.* 
elieved to be the largest capacity single discharge wheel 
imctcd. 

rther details see Figs. 183, 189 and 190. 
arly Development of Impulse Wheels* — As already pointed 
Chapter I, Fig;s. 6 and 7), water wheels of the impulse 
e among the earlier forms used. In the practical construc- 
^•ater wheels for commercial purposes in this country, the 

reaction turbine was^ how- 
ever, the earliest form of 
development This was 
because the reaction tur- 
bine was best suited for 
the low heads first devel- 
oped. As civilization ad- 
vanced from the more level 
country into the moun- 
tainous regions the condi- 
tions were found to radi- 
cally differ. In the form- 
er location large quanti- 
ties of water under low 
heads were available; in 
the latter, the streams 
diminished in quantity 
but the heads were enorm- 
ously increased. These 
IS demanded an entirely different type of wheels for power 
and the demand was met by the construction of the tan- 
rheel now so widely and successfully used in the high head 
: the West 

arliest scientific consideration of impluse wheds in this 
was by Jearum Atkins who, apparently, anticipated the 
f the wheels of the Girard type in Europe by" hi* design of 
bcel io 1853.t (See Fig. 163.) 




!. — Hunt Runner of The Rodney 
Hunt Macbloe Co. 



Ineineerinir Newfi/' March 29, 190e. 

rjttigential Watex Wheek" by John Richards, Cai«ier^i Htgazinep 




270 



Water Wheels, 




Other Americaa Wheels, 



%Ji 



In Atkins* first application for a patent (in 1853) he shows a 
lear conception of the principles of the impulse wheel. 

After describing the mechanical construction of his wheel, Mr. 
mcins says: 'The important points to be observed in the con- 
ruction of this wheel and appendages, are: First, that the gear- 
; • * ♦ should be so arranged as to allow the wheel's veloc- 
at the axis of the buckets to be equal to one-half the velocity 
the water at the point of impact, ♦ * ♦ 

"As the power of water, * * * is measured by its velocityp 
• it is obvious that in order that the moving water may 
imiinicate its whole power to another moving body, the velocity 
the former must be swallowed up in the latter* This object is 



^ 



Fig. ICO,— Shaw tnlgan Fallis Turbine Runner, 

.effected by the before-described mode of applying water to a wheel 
[in the following manner, the velocity of the wheel, as before 
|stat6df being one-half that of the water, 

**Let tis suppose the velocity of the water to be twenty- four feet 
[per second ; then the velocity of the wheel being twelve feet per 
Uecondr the relative velocity of the water with respect to the wheel, 
[cr the velocity with which it overtakes the wheel, will be twelve 
I feel per second. Now it is proved theoretically, and also demon- 
ed by cxpcrimentt that water will flow over the entire surface 
mi-circular buckets of the wheel with the same velocity 
di it first impinged against them, or twelve feet per sec- 
len, as the water in passing over the face of the buckets 



A 



2 72 



Water Wheels, 



has described a semi-circlej and as its return motion on lea\in| 
the wheel is in an opposite direction from that of the wheel, its 
velocity with respect to the ■wheel being twelve feet per second, 
and as the wheel has an absolute velocity of twelve feet per sec- 




Fig, lei.— Section Snoqualmle Falls Reaction Turbine. The Flatt Iron Wflrttj 

Company. 

ondj it is obvious that the absolute velocity of the water with t^I 
spect to a fixed point is entirely suspended at the moment of \n^\ 
ing the inner point of the buckets, its whole velocity, and const- j 
quently its whole power, having been transmitted to the wheeL" 




Early DevelofMnent of Impulse WheeL 



373 




^* ■'"■«* *^^*^ 



Ic 162. — &ection*Elldvatioii Snoqualmie FaHs Reaction Turblii« (The Ratt 

Iron Works Co.)* 



nil 




^gTlfiS,— Plati of Atkina Wheel and Wheel Case (1853). From Cksslei'B 
Magazine, Vol t. p. Hi, 



274 



Water Wheels. 



a. Moore bucket, 1874. 




& Bodd bucket, ISSa 




<u Boble EUipeoidal bucket ^ 
1889. 




b. Knight backets, 1870. 




/» PeltOD bucket^ 1$80, 

Fig. 164, — Buckets of TangcDtlal or Impulse Water WheelB. (Trans. 

Inst Mining H7ng. 1MB. 



Mr. Atkins* first application for a patent was rejected. After 
long illness, from which he finally recovered, he agfain applied for 
patent which was finally granted in 1875, Tlie Atkins* patents are* 
simply of historical interest as his inventions have bad little eff< 
on the practical development of the impulse wheel. 




American Inipuist; Whetils* 



n$ 



fj. Anierican Impulse Wheels, — ^The impiilse wheel found its 
test practical development in California where the conditions for 
jdevelopment of power made such a wheel necessary. The 
f tang^ential wheel, used on the Pacific Coast, was quite simple 
{instruction and the development of the backets, which began 
I the simpler flat and curved forms, was very largely based on 
ptperiniental method used for the development of the reaction 




(Pelton Water Wheel CoJ 



ijUO Foot Hea*!, 



e in the East, Experiments were made at the University 
Jifomia, by Mr. Ralph T. Brown, as early as 1883, and the 
in, published by the department was the earliest literature on 

fcntial wheels published in this country, 

!th the early development of the tangential bucket are con- 
the names of Knight, MoorCp Hesse, Pelton, Hu^, Dodd 
>oble, and many other inventors, whose wheels have become 
nown and widely used. The most extensive early develop- 



i 



276 



Water Wheels. 



ment of this wheel was by The Pelton Water Wheel Company 
whose work has been so widely known and used as to make the 
name '* Pelton Wheel" a common title for all wheels of the tangen- 
tial type. 

Some of the many forms of American buckets used are shown iir 

Fig, 164 with the approximate 
date of their invention or d^ 
sign. 

The general arrangement of 
a double 2Q0O H. P. unit, run^ 
ntng at 200 R P. M, under SOO 
foot head is shown in Fig, 165, 
This is one of three units in- 
stalled by The Pelton VValcf 
Wheel Company for The Tellu^ 
ride Transmission Plant of 0)1- 
orado* 

The wheels arc of cast $ltd 
fitted with steel buckets^ held 
in position by turned stcct 
bolts. They arc connected by 
a flexible coupling to a 1«200 
H, P. generator 

Fig. 166 shows the runncf oi 
an impulse wheel made bytk 
same company. This is 9 10 
in diameter^ and is designed to 
develop 5,000 H, P at 325 R- 
P M under an effective licad 
of 865 feet 

Fig. 167 shows the runner of an impulse wheel manufactured by 
the Ahner Doble Company. This runner was from the Doble Wa- 
ter Wheel Exhibit at the St Louis Fair and developed 170 H* F- 
at 170 R. P. M. under a head of 700 feet and generated direct cur- ^ 
rent for use on the intramural railway- 
In addition to the tangential wheels already described, a fewj 
manufacturers have developed wheels of the Girard type. Oii«* 
such wheel, designed and built by The Piatt Iron Works Company,' 
is illustrated in Figs, 168 to 171, inclusive. Fig. 168 is a section- 
elevaUon showing tlie arrangement and design of the guides ami 




Fig. 166.— Pf Hon Tanpential Water 
Wheel Runner- Designed for 5000 
H, P at 865 foot head and 225 R. 
P- M. t Pelton Water Wheel Co.) 




American Impulse Wheels. 



277 



fckets of the wheel. Fig, 169 shows a section through the wheel 
ll on the line of the shaft. In these figures W represents the" 
Itoer; BE the buckets; g, the inlet guides, and G, the gate by 
peh all or a portion of the guide passages may be closed and the 
ktr of the wheels reduced. The gate, G, is connected by the 
ings, Gfj with the rod, tt which is connected through the rocker 




Fig, 157. — Doble Runner. (ATiner-Dobl© Co.) 



I wtth the governor mechanism. The wheel or runner of this 
int is shown by Fig. 170, and a general view of the wheel is 
wn by Fig, 171, 

IS. Turbine Development in Europe. — Modem European tur- 

practice has been the development of the last twenty years, 

ppean manufacturers have approached the subject more on the 





278 



Water Whet:L*, 



basis of theoretical analysis than has heen done in America. The 
conditions of development have also been largely special and not 
under such uniform conditions as in America. The result has been 
the development of special designs for special locations and the 
rapid accumulation of a considerable experience under a wide range 



r 




^Ig. IC8.— E3iid Section aDd Elevatton, Glrard Impulse Turbine wiUi ^^ ( 
Tut©- CPlatt Iron Works Ca.> 

of conditions* While the radial flow turbines were the earlier typcj 
developed, European practice has been largely centered on the a3q3l| 
flow wheels of the Jonval type for complete turbines, and axil 
flow and radial flow wheels of the Girard type for partial turbin 
-under high heads. 




Afnerican Impulse WheeK 



279 



The axial flow turbine while simple In constructicm and low in 
cost is difficult to regulate and hence the demands of electrical de- 
velopment for dose regulation has given rise to a variety of mod- 
em designs which are summarized by Mr. J* W* Thurso essentially 
follows: 




W ^ffl "k^ 

[% Ua.^LoQgitudinal Section Glrard Impulse Turbine. (Piatt Iron W^&rksi 

CorapaufJ 



1st For low heads to 20 feet. Radiai inward flow, reaction tur- 
oincs with vertical shafts and draft tubes* 

2ncL For medium heads^ 20 to 300 feet. Radial inward flow reac- 
tion turbines with horizontal shafts and concentric or spiral cases 
tod draft tubes. 

jrd. For high heads over 300 feet. Radial outward flow, full or 
al action turbines (of the Girard type) with horizontal shafts, 



i^ 



'See "Modern Turbine Practice'* by J. W. Thurso. 




28o 



Water Wheek. 




often with draft tubes; 
also, modified impulse 
wheels of at taagcotiai 
type. 

The types of tar- 
bincs for low and mod- 
erate heads are mod- 
ificattoos of the Fran* 
CIS inward flow turbine 
Earlier European 
practice is perhaps wei: 
represented by Fig 
172 which represent* 
one of eight turbine^ 
installed by Messrs 
Escher, Wyss & Co 

Fig, 170— Runner of Glraxd Turbine. Type C, for the City of Geneva. 
High-Pressure Runner (Piatt Iron Works Co.) Switzerland These 

wheels are of the Jon- 
val type and operate 
under heads some- 
times as great as 12 
feet but during higti 
water the heads de- 
crease to about five 
and one-half feet 
The turbines consist ot 
three annular rings or 
buckets and arc so de- 
signed that the water 
is admitted to as many 
buckets as may be re- 
quired for economics^ 
operation under the 
very great differences 
in the condition c»f 
supply. The width of 
the inner and intcrme' 

PIf?, ITL^GeneraJ View of Girard Turbine with diate rings are cacH 
Cover Raised, (Piatt Iron Works Co,) ieventeen and thfCC- 




Turbine Development in Europe* 



281 



rs Inches^ and the outer ring is eleven inches, all meas- 

radially. The outside diameter of the wheel is thirteen feet, 

inches. The outer ring of guides is not provided with 

IS for excluding the water from the buckets but the i n termed i- 

inner rings can be entirely and independently closed. The 




171— Oo© of the ierenteen 210 II. P. Jonval Turbines at the Geneva 
Water Works. Built by Eacber, Wyea & Co. 

few closing the intermediate and inner rings consist of a flat 
in the form of a half ring, which lies on the top of the crown 

vertical curtain which hangs from the end of the plate and 
etes the closure of the other half of the bucket the openings 




282 



Water Wheclst 



of which are on the side of the same^ the water entering theBu- 
by a quarter- turn, 

Tliese turbines are used to operate the pump that furnishes 
water supply for the city of Geneva for domestic and maunfacin 
ing purposes. 




Fig. 173* The 1200 H. R Double Turbine at Chlvres near Geoem 
Eacher^ Wysa Jc Co. (Cassier^s Magazinep October, ISW.) 

Fig. 173 shows a pair of vertical turbines furnished by the sU 
company for Chlvres near Geneva, Here the fall in siimmer is 
feet and in winter 28 feet. The lower turbine will develop tj 




Turbine Development in Europe. 283 

. at 80 R, P. M. under the higher head, and under the lower 

the turbine above works with the lower one. 

ch turbine is cone shaped and divided into three compart- 

s in order to maintain the efficiency of the wheels at the same 

utions under the wide range in heads. 

pid advancement is now being made in turbine design both in 

:ountry and in Europe and the progress can best be known and 

2ciated by reference to the current technical press. 



I 



CHAPTER XIIL 

TURBINE DETAILS AND APPURTENANCES, 

139* The Rimner — Its Material and Manufacture. — The rnnners 
of most reaction turbines (see Figs. 136, 142 to 149, 151, 154 to 159, 
161) consist of hubSi crowns and rings, to which the buckets are at- 
lached. The wheels are sometimes cast solid, and sometimes built 
up. In built-up wheels the buckets are first cast, or otherwise 
formed, after which they are placed in a form or moulded, and tbe 
crownSj hubs and rings are cast to them. Turbine water wheels 
for low heads are usually made of cast iron or of cast iron with 
steel buckets. Wheels for high heads are frequently made of cast 
bronze or of cast steel. (See Figs, 158 and 159.) 

Probably the majority of cast wheels manufactured at the pr«- 
ent time are cast in one solid casting of buckets^ rings, hubs, and 
crowns. The buckets are formed by carefully prepared cores and 
in such manner as to leave them uniform in spacing and thickness, 
and smoothly finished so as to admit of the passage of water lhn>u| 
or between them without excessive friction. With wheels so 
no material finishing or smoothing of the surfaces of the bucket 
practicable, and the casting must come from the sand with a sal 
factory surface. In wheels cast solid, great care is necessary 
order to prevent serious shrinkage strains. This is partially ov' 
come by the use of soft iron, which results, however, in increJ 
wear of runners subject to the action of sand-bearing waters. 

With buckets cast separately, a higher surface finish of 
bucket is possible ; but when separate buckets are made and afti 
wards united, the runner must be strongly banded in order to gi^ 
it the necessary strength. Buckets of sheet steel, forged or 
to the desired shape, present a uniform and satisfactory surf; 
and when punched at the edges before casting, form a solid 
substantial wheeh 

The runners of Girard impulse wheels (see Fig. 171) are 
in the same manner as reaction runners. 

The runners of tangential wheels are usually made with scpti 
buckets and body, (See Figs. 167 and 168.) The bodies are 



Diameter of Runner. 285 

cording to the severity of the service, of cast iron, semi-steel, 
rged steel, etc. The buckets, dependent on the conditions of 
rvice, may be of cast iron, cast steel, gun metal, bronze, etc. The 
ckets, in the best wheels, are cast, shaped and polished and care- 
lly fitted to the wheel body. The bolt holes are then carefully 
illed and reamed and the buckets are bolted in position by care- 
lly turned and fitted bolts. 

140. Diameter of tfie Runner. — ^The diameters of reaction runners 
e measured at the inlet, and, when the buckets at the inlet are 
rallel and of one size, the determination of the turbine diameter 
a simple matter. (See Fig. 174, diagram A.) In order to give 
2 runner greater speed and capacity, the buckets are sometimes 
t back at a point opposite the bottom of the gate opening (see 
igram B), and the diameter of the runner opposite to the gates is 
iuced below that of the lower diameter. In such cases the edges 
the buckets are sometimes made parallel with the shaft but are 
ually inclined upward. In the latter case, the diameter of the 
leel at its top may be considerably reduced over its diameter at 
e offset. In such cases the cutting back of the runner may be one 
more inches at the bottom line of the gate with an inch or more 
clination to the top of the buckets, and the diameter of the wheel 
D and D'", diagram B, may differ from two to six inches or even 
ore. 

With wheels so constructed, there is considerable difference in 
ic practice of different manufacturers in measuring and listing the 
ameter of the wheels made by them. In some cases, the inside 
iameter, from ring to ring, D, diagram B, of the runner, is given 
$ the list diameter. In other cases, the diameter is taken at the 
iner angle of the offset as D'. In a number of cases the diameter is 
leasured at about the center of the gateway, D", and in other cases, 
IC diameter is measured at the upper and smaller diameter of the 
inner, D'". This variable practice leads to a considerable differ- 
ice in the nominal diameter of the various turbines as listed in 
e catalogues, and frequently a runner listed as of a certain diame- 
r by one manufacturer may be two to six inches larger than the 
nner of another manufacturer which is listed as of the same di- 
leter. This discrepancy in the method of measuring and listing 
5 diameter of turbine runners accounts, in some degree, for the 
parent greater capacity, higher speed or greater power of the 
eels of one manufacturer over those of another. 



^^^ 286 Turbine Details and Appurtenances. ^^H 

^^^" The practice of some of the American manufacturers of turbines, 

^M in measuring and listing the diameters of their wheels, is shown 

^H in Table XXV, In this table, all runners which are not cut back 

H and with edges parallel to tlie shaft, are classified as Style A, even 

H where they differ widely froin the form shown in diagram A, Fi^. 

■ 174. 

H All runners with buckets cut back are classified as Style B, tnn 

^^^^ where the bucket edges are parallel with the shaft. 

^^^P The diameters of tangential runners are usually measured 1^ 

^^^^ tween the centers of buckets or on the diameter of the circle on 

H which the center of the jet impinges on the buckets. 

H TABLE XXV% 1 

^M Praciiee of Various American Mannfaciurerii i>t MeamiHttg and Catalogi^^M 
^B Ui€ Diameter of Turbitm Water Whe^lB, H 


^^ M&niifactuTer. 


Name of Banner. 


Style, 


Poinl d 


^P Dayto0 Globe Iron Worke. . , 

Eodiaey Hiitit Machine Co. . . 
The James Lefiel h Co« ...... 

1 
\ 
' Piatt Iron Work i Co, 


A merican ...^*i .. #ii>fi»»*t 


A 

A 

B 

B 

B 

A 

A 

A 

B 

H 

B 

A 

H 

B 

B 

B* 

B 


D 
D 
J/ 
W 
D 
D 

D 

D 
D' 

W 

n^ 

D 


Sew American. i 


Especial New American. .... 
Impros^ed New American^ . . 
McCormick* .,...*«,*.*.*». 


Hunt. . ... * 


Standard Xrpffel. ,.,,,,. , , , . 


Special Leffel .............. 


Samnon .»... ,.,,,«..,. 


Improved SamEon. ,.,,..«.. 


Type A , 


1^ 8 Morgnn 8mith C4>, , , 


Tvpes B and C* .••.*. 


McGorniick' 


^H TheTrumpManufncturingCo. 
^f W el) man ^ Sea ver, Morgan Co. 


t^mith ........ ...,♦♦.,,,,.. 

Standard Tnimp* .......... 


Hiifh Speed Trninp* ..,,,... 


JolJj'M cCormick »,,,.,..«. 




I Fillet at angle. Dimneier mewflured just above. 

'Diameter of HsJnt-MLCjnniclc rutuiere \\h measured al the crown which pi* 
jects beyond the tips of the buckets and la essentially the same in diameiera^itp' 

•Diameter of the Smith -McC^irmick rutinera in meastired at the crown uhici 
projects beyond the tips of tbe bucket!^ and la essentially the ^aine in diatnaeri 
at D', 

« Diameter at D ie 20$ j^reater than at D". 

* Bucket or of high spt^ runner has parallel edges but is cut back as ebowii^ii^ 

141. The Details of the Runner. — The reaction rtinner will %*at 

in design with the conditions under which it is to operate and t) 

1 experience and ideas of its designer. In American practice t 



Details of the Runner. 



287 



lanufacturer usually constructs a series of runners of similar ho- 
nogeneous design; that is to say, each wheel of the series has all 
)f its dimensions proportional to that of every other wheel of the 
icrics, and is of similar design in all of its parts. 

On account of demands for considerable variations in speed or 
power, or on account of improvements which have been found de- 
sirable by reason of the demands of his trade, the manufacturer 
often designs and constructs several series of wheels, each of which 
is particularly adaptable to certain conditions which he has had to 
meet. (See Tables XXII and XXIV.) In such cases each series 
is best suited for the particular condition for which it was designed, 
and is not necessarily obsolete or superseded by the later series. 





Fig. 174. 



The curves of the runner buckets (see Figs. 13, 14, 133, 134, 136, 
J46-148, 175) must be such as to receive the jet of water from the 
nozzle or guides without shock, permit it to pass along the surface 
^f the buckets or through the passages in the runner with mini- 
'^um friction, and discharge it as nearly devoid of velocity as prac- 
ticable. 

To accomplish this, the relative position and relation of the 
^rves of guides and buckets must be carefully arranged. As the 
jet of water is always directed forward in the direction of the revo- 
lution of the wheel, the jet has an original velocity in that direc- 
tion, and, since the bucket must be so shaped as to give a continued 
contact, as the jet progresses and the wheel revolves, the portion of 
the bucket farthest away from the guides must be curved back- 
ward, and terminate at such an angle as shall permit the jet to 
pass away from the wheel with free discharge. (See Figs. 175 and 
128.) 



288 Turbine Details and Appurtenances. 





B 







Fig. 175.— Curves oY Buckets and Guides in Turbine Wheels. 





Vertical Turbine Bearings. 289 

tion runners are made either right or left handed as de- 
When looking at the top of the runner, if the wheel is de- 
to move in the direction of the hands of a watch, it is called 
handed wheel, and if it moves in the other direction, it is 
left handed wheel. (See Fig. 176.) 

buckets, hub, crown, and ring of the reaction runner must 
ufficient strength to receive the impact or pressure of the 
column of water under the working head, and to transmit 
rgy to the shaft through which it is to be transmitted to the 
ery to be operated. 

avy ring is usually desirable, both to give strength and 
to the outer edge of the buckets and also, under some cir- 
cumstances, to give the effect of 
a fly-wheel in order to materially 
assist in maintaining uniform 
speed. Floating blocks or other 
material, in spite of the use of 
trash racks, sometimes reach the 
turbine, and when caught between 
HAND LEFT HAND ^^it buckets and the case are apt 
—"Hand" of Water Wheels, to cause serious injury to the 

buckets, 
runner is attached to a shaft passing through the hub, to 
t should be closely fitted and strongly keyed to prevent its 
ig loosened by vibration and the strain of operation. This 
:ially necessary in vertical wheels, for if, under these con- 
the wheel becomes loosened and drops from the shaft, it is 
e practically destroyed. Impulse runners acting under high 
ire subject to heavy shocks and must be especially sub- 

i^ertical Turbine Bearings. — In all turbines where the dis- 
is axial and only in one direction, there is a reaction in the 
irection that tends to unbalance the wheel and to cause a 
n the direction opposite to the discharge. The leakage into 
:e back of the runner frequently produces a thrust in the 
J direction which may be wholly or partially relieved by 
s left in the runner, usually close to the axis. In large 
I attempt is made to balance these various pressures with 
rm of thrust bearing to sustain the difference in pressure 
vill occur under different conditions of operation. 



290 



Turbine Detaila and Appurtenances* 



In most single vertical turbines a simple step bearing is us«i 
The bearing itself in American turbines usually consists d£ a lig- 
num vitae block, turned to shape, and centered in a bearing block 
which is held firmly and centrally in place by the cross trees. Tbe 
bearing block is shown by T, and the cross trees by t, in Figs. 146, 
147 and 185. The bearing on the shaft itself is usually a sphcrica! 
sector, or some other symmetrical curve of similar form. In some 
cases this bearing is cut directly in the shaft itself, (See Fig. 14?) 
In others, a cast iron shoe is provided and attached to the shaft 
(See M, Figs. 145 and 184.) Above the turbine a second bearing 
is also provided (see T', Figs. 145 and 147) to keep the shaft \n 
vertical alignment* This bearing in American wheels is usually 





Pig. 177.^GeyUn (Pateat) Glass Suspension Bearing (It D, Wood t Oa).j 

of the type shown in Fig, 182, except that it is adapted to its vcr- j 
tical position. 

In the Geylin-Jonval turbine, manufactured by R* D* Wood] 
Company^ a patent glass suspension bearing is used, (Fig 177*) j 
This bearing is attached above the wheel (see T, Fig. 135) andh^j 
the advantage of being readily accessible. The turbine is here sus* j 
pended on a circular disc composed of segments of glass, B. H- 
Fig. 177, arranged with depressed divisions which form a conlifli*"] 
ous space around each segment of which the disc is composed, a'- j 
lowingt while the turbine is in motion, a perfect, free circitlalioul 
of the lubricating matter with which the space is filled.* The bfar-J 
ing is a true metallic ring, A^ firmly secured to the turbine sli*ftj 
which revolves on these stationary glass segments. 

In most European vertical turbines the step bearing is simply ^ 
guide, the main bearing being above the turbine and more fea^w; 
accessible than in the American form. 



•Catalogue of R. D. Wood i Cd., ISOl, p. lOT. 




Vertical Turbine Bearings. 



291 



5. 178 and 179 represent vertical bearings of this kind. In 

bearings C is a spherical sector so arranged as to take up any 

error in the vertical alignment of the shaft. Fig. 178 is a 

ball bearing; the hardened 
steel balls, AA, revolve 
between the special bear- 
ing plate, B and Bi. 

In Fig. 179 oil is pumped 
underpressure through the 
inlet, pipe OE, into the 
space A. By its pressure 
the bearing plate, B, is 
raised from its companion 
plate, B, and the oil es- 
caping between the plates 
lubricates them and over- 
flows through the overflow- 
pipe, 00. 

In both Figs. 178 and 
179 the height of the shaft 
is adjusted by the nut, N, 
which, after adjustment, is 
fastened securely in such 
position. 

At the power plant of 
The Niagara Falls Power 
Company a thrust or hang- 
ing bearing of this disc 
type, somewhat similar to 
Fig. 179, is used (See Fig. 
180). In this bearing the 
shaft is suspended to a 
revolving disc carried on 
a stationary disc. The 
discs are of close-grained 
charcoal iron of 25,000 
pounds tensile strength 
• 14" inside, 34'' outside diameter. The lower or fixed disk is 
led to a third disk with a spherical (3' 4" radius) seat. This 




178. — Vertical Suspension Ball Bear- 
ing.* 



eerkraftmaschinen von L. Quantz. 



292 



Turbine Details and Appurtenances. 



is to provide for an automatic adjustment for slight deviations from 
the vertical due to uneven wear of the discs and other causes. 

The bearing surfaces between the discs are grooved to allow a 
circulation and distribution of the oil over the surface. 

Three methods of lubri- 
cation, — forced, self, and 
a combination system^ 
were experimented with 
and the combination sys- 
tem finally adopted In 
the system of forced IuIk 
Hcation, the oil enters the 
fixed disc at two diamct* 
rically opposite points and 
is forced between the discs 
under 400 pounds pres- 
sure. Self-lubrication is 
accomplished by oil sup- 
plied at the inner circum- 
ference of the disc and 
on Pres- thrown outward by cen- 
trifugal force. 
The disc bearings arc 
enclosed in a case provided with sight holes through which the 
condition of the bearing as well as the temperature of the oi) can 
be observed, A thermometer and an incandescent light are sus- 
pended in the casing for this purpose. The oil is cooled by water 
circulating pipes inside the casing. 

The shaft is provided with a balancing piston (see Fig. 181) 
supplied with water from a pipe entirely independent of the pen- 
stock and under a head of 136 feet. This piston carries the greater 
part of the load, less than 2 per cent of the load being left to be 
carried by the oil- lubricated disc bearing described above. M 

143. Horizontal Turbine Bearings. — In horizontal wheels vari-" 
ous forms of bearing may be used according to the conditions and 
circumstances of their operation. When practicable the bearitigs 
should not be submerged and should otherwise be made as accessi- 
ble as possible. In such cases the forms of bearings may be tlie 
^ame as those used on other machines subject to similar strains- 



' WflBserkfftfimaflehfnen von L. Quants. 



Fig. 11^ —Vertical Suspension 
sure Bearing.* 








Horizontal Turbine Bearings. 



293 



many horizontal American wheels, where submerged bearings 
c necessary, lignum vitae bearings are used similar in type to the 
)pcr vertical bearing before mentioned (see T', Figs. 145 and 147) . 
jch a bearing is shown in detail in Fig. 182. In this bearing the 
laft, S, is sustained in position by the blocks, TT, which fit the 







Thruj^ 



I !l!i!k-i *V--K 

Secfion fhrough Boll Disk Oil Inlef 



Section through Oil 5i9hf Ho!©. 



Fig. 180.— Vertical Thrust or Hanging Bearing of the Ni- 
agara Falls Power Co. (See Eng. Record, Nov. 28, 1903.) 



esses of the cast iron bearing block, K, which in turn is attached 
a cross tie in the case or to a pedestal, P. The blocks, TT, are 
listed by means of the screws, BB, which, after adjustment 
locked in position by the lock nuts, LL. Such submerged 
rings are sometimes lubricated by water only, in which case op- 



294 



Turbine Details and Appurtenances. 



ft 



portnnity must be given for the free circuktion of the water In 
other cases the boxes are made tight and flow into them along tht 
shaft is prevented by stuffing boxes at each end of the main box^ 

the boxes being lubricated 
by forced grease lubrica- 
tion. 

Bronze boxes of the types 
used for other high grade 
machines are sometimes 
used for submerged bear- 
ings. In such cases great 
care ts necessary to pre- 
vent the entrance of grit-j 
bearing waters. Suchj 
bearings are lubricated byj 
forced oil or grease. 

In forced lubricatioa itj 
is desirable that both 1 1 
force and return pipe be I 
used so as to give visiblej 
evidence that the lubri'^ 
cant is actually reactiing| 
the beari ng* In some 
cases bearings that woUd 
be otherwise submerged 
are made accessible at allj 
times by metallic tub 
(see Fig. 322) used 
manholes. 
Where the turbine is placed horizontally, gravity can no long 
oflfset the thrust caused by the reaction of the turbine when th 
discharge is in one direction, and the thrust must therefore be ove 
come by the use of some form of thrust-bearing. Where other con 
ditions permit, it is quite common practice to install two turbina 
on a single horizontal shaft, having their discharges in opposite dH 
rections, in which case the thrust of each turbine is overcome 1 
the thrust of its companion (see Figs. 153, 160 and 316)* In manj 
cases, however, the arrangement, size and capacity of the whcei 
to be used are not such as will permit the use of twin turbines an^ 
thrust-bearing, and other means of taking up the thrust must 1 
tjrovided. 




Pig, 181, — Section of Turbine used m new 
Power ilouse of The Niagara Fall^ Power 
Oompapy, showing Balancing Hydrauliti 
piston nsed to in&lnin Turbine and Shaft 
(Eng. Record, Nov. 28, 1903,) 





onzontal Turbine bearififfs. 



295 



144, Thmst^Bcaring in Snoqualmie Falls Turbine, — In the Sno- 
<iualmie Falls Turbine, manufactured by The Piatt Iron Works 
Company (see Figs. 161 and 162), the device for taking up the 
thrust is thus described by the designing engineer, Mn A. Giesler:* 
**Sing!e-wheel horizontal-shaft units are relatively infrequent in 
turbine practice, especially in large sizes, where the thrust of a sin- 
gle runner is large enough to require careful consideratian. The 
thrust is made of two parts: (1) that due to the static pressure or 
effective head of water at the various points of the runner surface ; 
and (2) that due to the deflection of the water from a purely radial 




/^]r\ 



FSf. l82.^HorlzontaI Lignum Vltae Bearing as Used In American Turbines. 

path through the wheel. As concerns the first part, the front face 

^f the wheel is pressed upon by a pressure varying from the supply 

head at the outer circumference to the discharge pressure (vacuum) 

^t the inner edge of the vanes* which latter extends over the whole 

^^ntral area of the runner (and shaft extension). The rear face of 

^^c runner is subjected to the pressure of water leaking through 

'he radial air-gap between casing and runner, substantially equal to 

^"^ supply head. This greatly over-balances the pressure on the 

f^Ofit face, and the resultant thrust is to the right in Fig. 161 (to- 

^^t*d the draft tube). The discharge ends of the vanes, being 

^^^ed transversely, also have a pressure component directed to- 

* See "Englnetrlng News'' of Marcb 29. 190e. 




2^6 



Turbine Details and Appurtenances* 



ward the right. The velocity effect produces a thrust directed to* 
ward the left, but this is very small and does not materially reduce 
the pressure tlirust. 

*'Ey far the larger part of the pressure thrust is eliminated by 
venting the space back of the runner into the discharge space. Six 
holes through the wheel near the shaft, indicated in Fig. 161, have 
this function. The water leaking in through the air-gap is continu* 
ously discharged through these vents into the draft*tube, and the 
accumulation of any large static pressure back of the wheel 
[hereby avoided. 

"The average pressure on the front of the runner, however^ if 
always lower, and the resultant thrust is therefore toward the draftJ 



|i /7^'r: 4 




Crp«* Section. 



Lon^'itudinol SvcHon* 



Fig. 1S3.— Thrust'Bearing Snoqualmle Wheels. 




tube, though its amount varies considerably, being greatest for fu^ 
gate opening. This thrust is taken up by the balancing piston in 
mediately back of the rear head of the wheel case, and the tiltimat^j 
balance and adjustment of position is accomplished by the coU 
thrust^bearing behind the balancing piston. 

"The balancing piston is a forged enlargement of the shaft, 
ished to a diameter of 17 inches, which works in a brass sleeve ! 
in a hub-like projection on the back of the wheel-hotising. The ifl 
side of the sleeve has six circumferential grooves, each one inch wid 
and one-quarter inch deep, as water packing. The chamber in fn 
of the piston communicates by a pipe (containing a strainer) witkj 
the supply casing of the water-wheel, and therefore reccivea tS 
full pressure of the supply head. The chamber back of the piston' 



— *- — 



Thrust-Bearing in Snoqualmie Falls Turbine. 297 

is drained to the draft-tube, so as to carry off any leakage past the 
piston. The device thus produces a constant thrust on the piston. 
directed toward the left. By throttling the pressure pipe this 
thrust can be adjusted as desired. 

"The thrust-bearing shown in Fig. 161 and in detail in Fig. 183 
:onsists of a group of four collars on the shaft, working in a babbit- 
ed thrust-block which is bolted to the back of the wheel-housing. 
[Tie collars are formed on a steel sleeve which fits over the shaft 
nd is bolted to the rear face of the balancing piston ; this makes 
t possible, when the collars are worn out, to renew the bearing by 
ismounting the thrust-block and placing a new sleeve. The 
hrust-bearing is lubricated by oil immersion. An oil chamber is 
ored in the block and communicates by numerous oil holes with 
he bearing faces ; a constant flow of oil is maintained by means of 
►il-supply and drain-pipes. Concentric with the oil chamber and 
»utside of it a water chamber is cored in the block. Cooling water 
3 supplied to this chamber by a pipe from the pressure side of the 
urbine, and drains from the top of the bearing through a drain-pipe 
the draft-tube. A U-pipe attached at one side of the bearing forms 
:onnection between the water chambers of the upper and lower 
lalves of the block. This detail avoids making the connection by a 
lole through the joint face, which would allow leakage of water 
nto the oil-space and into the bearing. 

"The balancing piston is so proportioned and the pressure supply 
)ipc is throttled to such a point as to give exact balance (i. e., with 
:cro thrust in the thrust-bearing) at about half to five-eighths the 
uU output of the wheel. At larger power there will be an unbal- 
mced thrust to the right, and at smaller output to the left, which 
ire taken by the thrust-bearings. The maximum thrust on the 
:olIars is about 25,000 lbs. The collars are 2^^ inches high (2% 
nches effective) by 1314 inches mean diameter, giving a total effec- 
ivc bearing area on four collars of 418 sq. inches. The maximum 
x)llar pressure is thus about 60 lbs. per sq. in." 

145. The Chute Case. — ^The chute case (see Figs. 146, 147 and 184) 

onsists of the fixed portion of the turbine to which are attached 

he step and bearings of the wheel (T), the guide passages (g) 

rhich direct the passage' of the water into the turbine bucket, and 

le gates (G) which control the entrance of the water, and also 

le case cover (C). The case cover keeps the wheel from contact 
18 



293 



Turbine Details and Appurteoaoces. 



with the water except as it passes through the guide and gates* To 
the chnte case is usually attached the apparatus and mechanism for 
manipulating or controlling the position and opening of the gate. 
{A. P, Gn, etc) In vertical turbines a tube, d, is usually attached 
to the lower ring, forming a casing in which the lower portion of 
the turbine revolves an»l on which the bridge tree, t, holding tlic 

step bearing is attached 
When this lube is no long* 
er than one diameter it is 
u?sually called the turbine 
tube; but when it is con- 
siderably extended, it is 
termed a draft tube. 

The design of the tur- 
bine tube depends largely 
on the character ot the 
wheel. Some wheels dis- 
charge downward and in- 
ward, some almost entire- 
ly downward^ some down- 
ward and outward, and in 
some cases, the wheel dis- 
charges in all three direc- 
tions. For the best re- 
sults the tube should be 
so designed that the water 
from the wheel shall 
received by it with 
radical change of velocii 
and so that the remaininl 
velocity will be gradually 
reduced and the wat< 
discharged at the low« 
practicable velocity. 
The chute case and its appurtenances should be so designed tin 
the water will enter the bucket with the least possible shock or 1 
sjstance at all stages of gate and with a gradual change in vclocit; 
and will discharge from the buckets into the turbine tube with 
little eddying as possible and be evenly distributed over the cr 
section of the tube so as to utilize the suction action of an unbrok 
column of water The case must also be designed of sufEtie 




Fig. 184. 



k 



The Chute Case. 



299 




185. — Section Swain Turbine. 



o sustain the weight of the turbine wheel and so that the 
igs are accessible and can be readily replaced or adjusted, 
gement of the case must also be such that the openings 
he wheel and the case are as small as practicable and the 

line of possible leakage 
will be as indirect as pos- 
sible so as to avoid leak- 
age loss. 

Most chute cases are 
either cast or wrought 
iron. Cast iron usually 
lends itself to a more sat- 
isfactory design for receiv- 
ing and passing the water 
without sudden enlarge- 
ment and opportunities 
for losses by sharp angles 
and irregular passageways. 
Wrought iron, while not 
always lending itself read- 
ily to designs which elim- 
iuch losses, possesses much greater strength for a given 
tiich is a g^eat advantage under some conditions. 
rbine Gates. — ^Three forms of gates are in common use 
lling the admission of water into reaction turbines. The 
^te consists of a cylinder closely fitting the guide that 
ition admits or restricts the flow of water into the buck- 
184 is a section of a turbine of the McCormick type, 
ired by the Wellman-Seaver-Morgan Company, having 
this type, GO, between the guides and runners, which is 
sed in the cut. The gate is operated by the gearing. Or., 
>es it into the dome, O, through connection with the gov- 
't, P. This same type of gate is used over the discharge 
agara-Fourneyron turbine (see GO, Fig. 134), over the 
e Geylin-Jonval turbine, GG, Figs. 135 and 137, and be- 
: guides and buckets of the Niagara turbine, shown in 

Red form of the cylinder gate is that used by the Swain 
lompany (see Fig. 185), which is lowered instead of being 
) the dome as in Fig. 184. 



300 



Turbine Details and Appurienances, 



A similar modification, called a sleeve gate by its desi^er. J, W. 
Taylor, is shown in Fig, i86. 

When partially closed the cylinder gate causes a sudden contrac* 
tion in the vein of water which is again suddenly enlarged in enter- 
ing the runner after opening the gate, (See Fig. 1 88.) These con- 
ditions produce eddying which results in decreased efficiency at 
part gate. (See Figs, 185 and 186.) 

The wicket gate, when wdl 
made, .is perhaps the most satisfac- 
tory gate, especially for moderate 
or high heads. It can be readily 
balanced and should be made witl 
perhaps a tendency to drift shut, 
so that should the governor mech- 
anism break or become disabkfl, 
the gates will drift shut. These 
gates are illustrated by GG, 
Figs, 147 and 148, which illustraif 
the wicket gate of the Samsor. 
turbine of The James Leffel ^ 
Company, and Fig* 187 which 
shows the wicket gate of the Well 
man-Seaver- Morgan Gompaoy 
In both cases the wickets are con- 
nee ted by rods with the eccentric 
circle and through an arm and 
section with the gearing Gr, 

Figs. 145 and 146 show the wick- 
et gate of the Improved Nctf 1 
American, and Figs. 161 and 1611 
show the wicket gates of the Sno- j 
qualm ie Falls turbine, nianufacl*j 
ured by The Piatt Iron Wori 
In both the New American ai* 
Sleeve Snoqualmie wheels^ the gates a^ 
moved by a gate ring (see 
Fig. 145). Figs. 189 and 190 sh 
the details of the wicket gates and connection of the same to 1 
gate ring of the Snoqualmie Falls Turbine. 

The tendency to produce eddying is much rediiced in well 
signed wicket gates, although the sudden enlargement of the rt-j 




Fig. 



186.— Section Taylor 
Gate. 



^^m 



Turbine Gates. 



301 



vem at part g^ate undoubtedly reduces the efficiency of the 

(See Fig. 191, A and B,) 
register gate (see G, Fig> 192) consists of a cyhndcr case 
pertures to correspond with the apertures in the guides, g, 
so arranged that, when in proper position, the apertures rcg- 
nd freely admit the water to the wheel, and is also so con- 
id that when properly turned the gate cuts off the passage 
ftely or partially as desired, 

»iderable eddying is produced by the partially closed reg* 
ite, with a consequent decrease in part gate efficiency, (Sec 

Fig. 193.) The cylinder 
gate is usually the cheapest 
and most simple form of 
gate» but the wicket gate, 
if properly designed and 
constructed seems to ad- 
mit of the entrance of 
water into the bucket with 
least possible resistance 
and eddying, and in the 
most efficient manner. 
This form of gate is the 
most widely used in high- 
grade turbine construc- 
tion at the present time, 
although the cylinder gate 
is largely in use and has 
given satisfactory results. 
In some cases the pas- 
sage of water is restricted 
or throttled by the use of 
irfly valve, either in the inlet or in the turbine tube. This 
ts the inlet or discharge and regulates the head in a very 
ent manner, but may be reasonably satisfactory where econ- 
[ water is unnecessary. 

npulse wheels the gates are usually so arranged that the 
passages are opened one at a time instead of all opening par- 
is in part gate conditions with the reaction wheel. This re- 
a less loss in the cddyings caused by part gate. Fig. 194 
the type of gate used by The Piatt Iron Works in their Gir- 




L87. — Wicket Gate of the WeUmaii 
Seaver Morgan Co. 




3Q2 



Turbine Details and Appurtenances. 



ard turbines where the guide passages are arranged symmetricalH 
in three groups about the wheel. In the tangential wheel, where 
a single nozzle is used, the most efficient method found for redu- 
cing the opening is with the needle as illustrated in Fig. 195. This 
figure shows a cross section of Oie Doble needle nozzle, a form 
which gives a high velocity coefficient under a very wide range oi 
opening. The character of the stream froni a needle nozzle when 

fi^reatly reduced is shown by Fig- 
196 where the clear and solid 
stream gives evidence of high effi- 
ciency. If the flow of water 
through the nozzle is regulated by 
throttling the water with a valve 
before it reaches the noziki 
very low efificicncy results. 

147. The Draft Tube.— The r 
action wheel is of particular ad 
vantage under low heads oa ad 
count of the fact that it can mq 
efficiently under water, and then 
fore, under backwater condition 
can be made to utilize the full hca 
available. It is not nece^^aryj 
however, to set the reaction whed 
low enough so that it will be beM 
water at all times for the principle 
of the suction pipe can be utiliza 
and the wdieel set at any reasoo' 
able distance above the tail waici_ 
and connected thereto by a if* 
tube which, if properly arrange^ 
will permit the utilization of the full head by action of the drafl 
or suction puil exerted on the wheel by the water leaving tb 
turbine through the tube from which all air has been exhausted 
The water issuing from the turbine into a draft tiibct which at lb 
starting is full of air, takes up the air in passing and soon estal? 
lishes the vacuum necessary for the draft tube effects. The f«"C 
tioo of the draft tube is not only to enable the turbine to utiliii 
by suction that part of the fall from the wheel discharge to tbct*l 
water level, but it should also gradually increase in diameter so J 




Ftg. l&S.— Stiowing Cylinder Gate 
Partially Open and E<3 dies Caused 
by Sudden Contraction and En- 
largement of Entering Vein of 
Water. 




Fig. 189.— Showing Relations of Gate Guides and Buckets in Snoqualmie 
Falls Turbine (Piatt Iron Works Co.). 














SsctJon A-B- 



1g. 190. — Showing Rigging for the Operation of Wicket Gate in Snoqualmie 
Fpll9 Turbine (Piatt Iron Works Co.). 



3^4 



Turbine Details and ADpurtenaoceSi 




A. Gate wide open. B. Pan i:il gate. 

Fig, 191. — Showing Couditton of Flow Through Open and Partiallj 

Wicket Gatea. 



^y 



to gradually decrease ihe 
velocity of the water after 
it is discharged from the 
turbine wheel, thus enab- 
ling the turbine to utilijc 
as much as possible of thi^ 
velocity head with whiclj 
the water leaves the tup 
bine. It should be not^ 
that a partial vacuum isl 
established in the draft 
tube and, therefore, tfce 
draft tube must be stron 
enough to stand the c^te I 
rior pressure due to the I 
vacuum so created. Inor-I 
der to perform its functions j 
in a mo re satisfactory man- 1 
ncr, it must also be madc^ 
perfectly air tight 
One of the great advantages in the use of the draft tube is the 
possibility, by its use» of setting the wheel at such an elevation 




ng. 



192.— Register 
Works 



Gate 
Co.). 



(Piatt Iron 




Turbine Gates. 



305 



tail water that the wheel and its parts can be properly 
by draining the water from the wheel pit. Otherwise it 
accessary to install gates in the tail race and pumps for 
'Ut the pit in order to make the wheel accessible. The- 
thc draft tube can be used of as g^eat length as the suc- 
>f a pump, and this is probably true of draft tubes for 
very small wheels. Practically, the 
draft tube should seldom be as 
long as 20 feet, especially for large 
wheels, for its success in the util- 
ization of the head depends on the 
maintenance of an unbroken col- 
umn of solid water, which is diffi- 
cult to maintain in large tubes. As 
the size of the wheel increases the 
difficulties of maintaining a vac- 
uum increase and the length of the 
draft tube should correspondingly 
decrease. It is practically impos- 
sible to maintain a working head 
with large turbines through long 
draft tubes with the turbine set at 
great distances above the water. 
Long draft tubes should, as a rule, 
be avoided and in all cases where 
draft tubes are used, they should be 
as straight and direct and as nearly 
vertical as possible. It is the prin- 
ciple of the draft tube that per- 
mits horizontal shaft wheels to be 
utilized, as otherwise, with this 
chinery, only a small portion of the head could be used 
j^e under normal conditions, for such wheels being often 
ected to the machinery are, of necessity, placed above 
ter. The draft tube is commonly of iron or steel, but in 
re concrete construction is used the draft tube may be 
ictly in the concrete of the station or wheel foundations, 
ourneyron turbine Boyden used what he termed a difFu- 
Fig. 197.) The main purpose of the diffuser, and of the 
e as well, is to furnish a gradually enlarged passage 
lich the velocity of the water as it leaves the wheel is 




lowing Eddying Caused 
1 Closure of Register 



3o6 



Turbine Details and Appurtenances. 




B'lg* 194. — Gates and Guides of Qtrard Impulse Turblae. (Turbine Dwlp 
ss Modified for Close Speed Reflation, G. A. Buvinger, Froc. Am. Soc 
M. E., Vol. XXVI Ij 



I 




Fig. 19S. — Cross-section of Doble Needle NozEle.' 



* From Bulletin No. 6« Abner Doble Co. 




The Draft Tube, 



307 





Fig. 196. — ^Stream from Doble Needle Nozzle** 

so gradually reduced as to 

enable the velocity head to 
be milized in the wheel, 
thus saving head which 
would otherwise be lost 
It has already been noted 
that impulse wheels of the 
Pel ton and Girard types 
cannot operate satisfactor- 
ily submerged, and must 
be set at such positions 
that they will be above the 
tail water at all times. In 
many localities where the 
variation in the surface of 
tail waters is considerable, 
ans a large relative loss in the head utilized and that this 
wheel will therefore not be practicable except under high 



197. — ^BoydeD D Iff user 



1 Bulletfn No G« Abner Doble Co. 




3o8 Turbine Details and Appurtenances. 

head conditions and where the loss entailed by the rise and fall of 
the tail water will be inconsiderable. An attempt has been made, 
however, to so design a draft tube that a vacuum will be established 
and maintained below the wheel, in such a manner, however, that 
the water will not come in contact with the wheel. The vacuum is 
so maintained as to hold the water at an established point just below 
the wheel, thus permitting the wheel to utilize the full head except 
for the small clearance between the wheel and the water surface in 
the draft tube. This arrangement is shown in Figs. 168 and 171, as 
applied by The Piatt Iron Works Company to a Girard turbine. 



CHAPTER XIV 

HYDRAULICS OF THE TURBINE. 

148. Practical Hydraulics of the Turbine. — It is not the purpose 
of this chapter to consider mathematically and at length the princi- 
ples of hydraulic flow in relation to the curves of guides and buckets 
and the effects of such curves on the power and efficiency of the tur- 
bine. These relations are expressed by long and involved equations 
of considerable interest to the engineer who is to design and con- 
stract the turbine but of little practical value to the engineer who is 
to select and install it in a water power plant. Few of the designers 
of American wheels have given much attention to the involved 
mathematics of hydraulic flow in the turbine and the designs of 
most American wheels are based on the results of experiment and 
broad practical, experience. The designs of Swiss and German 
wheels are, to a much greater extent, based on mathematical 
analysis. It is an open question whether the best work of either 
American or foreign manufacture shows any marked superiority 
in comparison with the other. The results actually attained in the 
nianufacture of wheels in this country seem to show that the 
American practice in wheel design will give equal and even more 
uniformly satisfactory results than the European methods, — at 
^east as carried out by foreign engineers under American condi- 
tions. 

Correct theory must be the basis of all successful work. The 
theory of the experienced man may be unformulated and unex- 
pressed, but correct design has always a correct theory as its basis 
^vcn if unrecognized as such, and such a theory properly applied will 
lead to correct results. On the other hand, formulated theory will 
lead to correct results only as far as the theory is correct and takes 
into account all controlling or modifying factors and is properly ap- 
plied. A correct theory, carefully formulated and properly applied, 
^nnot fail to be of g^eat service to the engineer in extending his 
Experience to wider fields. Scientific study and mathematical an- 
^ysis of the turbine, based on wide experience and careful experi- 
ments, can but lead to the accomplishment of better results than 
have yet been attained. 



3IO 


Hydraulics of the Turbine. 




An understanding of certain laws of flow through turbines as con- 


firmed 


by both theory and practice is essential to a proper compre^ 


liension of the principles which should govern the selection and 


installation of such wheels and these laws are considered 


in this 


chapter 






149- 


Nomenclature used in Chapter. — In the discussion 


in this 


chapter 


the letters and symbols used have the following 


signifi- 


cancc: 






a 


= Area of gate orlfioe or ortScea 




B 


= Angle of defleniion of jet. 




^m 


= Supplement to anj^le of deflection = 180' — ci. 




^M 


— Diameter of wheel in inches. 




H 


= Energy in foot pounds per second. 




^B 


^ Force producing preesLire or motion. 




^m 


= Aeceierfltioa of grnvity* 




^1 


= Effective head at the wlieel. 




^B 


=i Numljer of revolutions per minute* 




^M 


= Number of revolutions per minute for hend hj. 




^M 


= Ratio of circumference lo diameter ^ 3;1416 




^m 


^ Home powers of turbine at any given head. 




^M 


— Horse power of turbine at head hj< 




^M 


= DiBcltar^e In cubic feet per Becond at any given head* 




^M 


= Discharge in cubic feet per second at head h^. 




^B 


= Interna) radius of wlvee!. 




■ 


s= External radius of wheel. 




k. 


^ Space passed tti rough by force acting.* 




^B 


= Velocity of wheel at gate entrance* 




^1 


= Velocity of wheel at point of discharge. 




H 


= Theoretical spouting velocity due to head = r %n 




^1 


= Velocity of the periphery of the impeller, in feet per second. 




^B 


= Al^isolule velocity of water entering the wlieel. 




^" 


= Absolute velocity of water leaving tlie wh^^el. 


J 


W 


=i Relative velocity of water entering ihe wheel. 


1 


^ 


= Relative velocity of water leaving the wbeeL 


I 


^^ 


= Average velocity. 


■ 


B 


= Total weight per second. 


I 


^ 


= Weiglit of unit of water = 62.5 lbs. 


.,■ 




ss Batio peripheral velocity of wheel to epouting velocity of water ^r H 




TURBINE CONSTANTS, 




C 


= Coe0cient of discbarge of gate orifice or orificea. 




A 


= Constant relation of turbine diameter and apeed* 




K 


= Cbnstant relation of turbine diatneter to discharg@u 




Kt 


= Constant relation of turbine diameter to powder. 




K, 


= Constant relation of peripheral velocity. 




K4 


— Doefilcient of relation of turbine speed and discharge. 




^H 


— Ooeflicient of relation of turbine power and speed* (Specific 


q.Md.1 



First Principles. 311 

C50. First Principles. — In the utilization of water for power pur- 
ses it is the first principle of design that the water should enter 
r wheel tvithout shock and leave it without velocity. This should 
interpreted to mean that the approaches of the water to the wheel 
ist be such as to cause no loss by undue friction or by sudden con- 
ctions or enlargements (inducing eddies and other sources of lost 
^rgy)» 2ii^d that all shocks should be confined as far as possible to 
t action on the wheel buckets leaving the full amount of energy, 
d consequently the velocity, to be entirely converted to power 
erein. 

In gravity wheels, illustrated by the various overshot wheels for- 
erly so extensively used for water power purposes, the water 
ould enter the wheel at the lowest practicable velocity and should 
: retained in the buckets until the buckets have made the greatest 
)ssible descent from the nearest practicable approach to the eleva- 
on of head-water, to the nearest practicable approach to the eleva- 
3n of the tail water. Part of the velocity of approach to the wheel 
ay be utilized by impact on the buckets but the entire energy re- 
laining in the water as it falls or flows away from the wheel is lost, 
id cannot be further utilized in the wheel. 

The greater the reduction in velocity, the greater the proportion 
f energy that can be utilized, but there comes a limit beyond which 
is not practicable to go. This limit varies with different condi- 
ons and may be the result of too great expense in the building of 
ceways or in the construction of the machine itself. A point will 
- reached where the friction expended in the large machine needed 
reduce the velocity will consume more energy than would be lost 
inducing a higher velocity. These losses must be equalized. In 
actice it is found that about two or three feet per second are satis- 
:tory velocities at which to reject or discharge the water used by 
itors. These velocities represent heads of from .062 to .014 feet, 
from three-quarters to slightly less than two inches. The veloc- 
'of discharge must, however, be fixed for each individual case and 
:er all conditions are fully understood and considered. 
151. Impulse and Reaction. — A jet of water spouting freely from 
y orifice will acquire a velocity (see Eq. 9, Chap. II). 

(1) V = v/^ 

i will possess energy in foot pounds per second (see Eq. 10, 
ap. II) as follows: 



312 



Hydraulics of the Turbine, 



The energy of the jet leaving the orifice is the product of a fort«j 
F, which acting on the weight of water^ qw, for one secotid gives ^ 
the velocity v. 

The space passed through by the force in one second, in raisin 
the velocity from to v is (see Eq. 6, Chap. II) 



(3) 



8 = vat=y 



and the work done in foot pounds is therefore 
(4) E = FS = ^ 

From Equations 2 and 4 therefore 

w 






The force, F, is exerted, by reaction on the vessel of which the 
orifice is a part and may produce motion in that vessel if it be fr« 
to move, or it may produce motion in another body by impube 
through the extinction of the momentum of the jet in impingiaf 
against it 

These equal and opposite forces are well shown: 
1st. By the force required to sustain a hose nozzle against the 
reaction of a fire stream, and 

2nd, By the force of the jet, from the nozzle so sustained when 
exerted against any object in its course. 
These conditions are illustrated by Figs. 198 and 199, 
The force, F, which may be exerted by a jet impinging against 
a surface depends on the momentum of the moving stream of wa- 
ter and is directly proportional to its velocity. It is also a function 




Fig. Ids, 




The Impulse Wheel. 



3i3 



the angle through which the jet is deflected. If friction be ig- 
>red, the stream will be deflected without change in velocity, and 
e force exerted against the surface in the original direction of the 
t will be equal to the momentum of the original stream less 






Fig. 201. 



■9 



Fig. 202. 



Fig. 200. 



the component, in the original direction, of the momentum of the 
diverted jet. (See Fig. 200). 



(7) 



F = 






If the jet impinges against a flat surface (see Fig. 201) 
a = 90®, Cos a: = and 

(8) F=3^ 

g 

If the jet is deflected i8o* by means of a semi-circular bucket 
(see Fig. 202) 

Cos 180® = — 1, and therefore 

(9) F=22^ 

g 

152. The Impulse WhccL — Impulse water wheels utilize the im- 
pulsive force of a jet impinging against buckets attached to the 
•ircumference of the wheel. The bucket must move under the 
^pulse in order to transform the energy of impact into work and 
he ratio of v', the Velocity of the periphery of wheel, to the velocity 
of the jet is indicated by ^ 



(10) 



y' 
fl) = — and v' = ^ ▼ 
▼ 



19 



3H 



Hydraulics ot the Turbine. 



I 



In determining the force, F, exerted upon the moving bucket, the 
relative instead of the actual velocity of the jet mtist be considered _ 

and it is readily seen that 
value of the relative velocity v^' 
will be as follows: 




(11) 



▼t= ▼— gj V ^(1 ^^)T 



-^^ The relative weight of water] 
that strikes a single bucket perl 
second wilUalso be less on ac- 
count of the movement of the 
buckets, but as new buckets con- 
stantly intercept the path of the 
jet the total amount of water, 

effective is equal to the total discharge of the jeL Hence frofi 

equations (7 and U) 



Fig. 203. 



(12) 



F ^ (1 - COB a) 3^ {1 - <p} 



The work done upon the buckets per second is equal to the fo 
F, times the distance <f> v through which it acts, i* e# 



(IS) 



E = F ^ V = (I ■ 



Qoea) (1 — <p) -^^ — ff ? 



This is a maximum when Cl — 4') ^ is a maximum the soluti 
of which gives ^ = .5 

Substituting ^-.5 and i»=i8o*, in equation (13), there is 
tained 

That is, E equals the entire energy of the jet (see equation 2), an 
hence the theoretical efficiency when ^»=^o.S is lOO per cent 

Another criterion for maximum efficiency is that the absolati 
velocity of the water in leaving the bucket must be zero. 

When a ^180'', the absolute velocity with which the 
leaves the bucket is evidently the velocity relative to the buck 
minus the velocity of the bucket or 

(15) v^ = (1 — ^) T ^ ^v s= V — 2f» V = 

This gives 

<p = 0.5 




EfiFect of Angle of Discharge on EflBciency. 315 

155. Effect of Angle of Discharge on Efficiency. — In an impulse 
wheel it is not practicable to change the direction of the water 
through 180** as it would then interfere with the succeeding bucket, 
r must hence be less, than 180** and the absolute velocity of the 
water in leaving the buckets cannot be zero. The loss from this 
jonrce is small as a may differ considerably from 180* without 
much effect on the bucket pressure and hence on the efficiency. 
For example, — ^the ratio of actual pressure when a is less than 
i8o* to maximum possible pressure with a .=180** is (see Fig. 203). 

If/Jr:8^ a = 1720, and ^— ^|2i£. = .W6 

showing only 0.5 per cent reduction. The effect on the efficiency 
is in the same ratio. 

Fig. 204 illustrates the flow of the water in entering and leaving 
the bucket with all velocities pven relative to that of the bucket. 
The jet leaves the bucket as shown with a relative velocity of (i — <^) 
V. If this velocity is combined graphically with the velocity of 
the bucket, ^v, the true absolute residual velocity v, of the water 
will be obtained. The efficiency is evidently maximum when ^ has 
a value which makes v^ a minimum. This condition can readily 
be shown to maintain when the triangle is isoceles or when 

(17) ^v = (l — ^)v 

which gives 

^ = 0.5 
as obtained by two other methods and here shown to be indepen- 
dent of the angle p. 

The absolute path of the water in space is shown by ABCD Fig. 
204, and the magnitude of this velocity is shown below in curve EF 
where ordinates are absolute velocities along the tangent lines to 
curve ABCD at the point directly above. These curves are based 
on the assumption that ^==0.5 and the bucket is semi-circular in 
cross section as shown. 

The theoretical considerations thus far discussed are modified by 
the frictional resistance which the bucket offers to the flow of wa- 
ter over its surface and by the spreading of the original jet from 
its semi-circular section to a wide thin layer in leaving the bucket. 



3i6 



Hydraulics of the Turbine- 



Further loss no doubt takes place as a result of the fact that the 
bucket is in its assumed position at right angles to the direction 
of the jet only at one instant during its rotation. Upon entering 




F(g- 204. 



and leaving the jet it is inclined considerably to this direction and 
doubtless operates less efficiently. These conditions result in ^ 
much greater drop in efficiency than the above analysis would 
seem to indicate, 

154. Ruction WheeL — ^Thc flow of water through the buckets of 
a reaction wheel is less easily analyzed than in the case of the ini* 
pulse wheeL The chief difference in the two types of wheels arises 



Reaction Wheel, 



317 



om the fact that the reaction wheel is "filled" and hence the ve- 
Kdty of the water relative to the buckets at any point does not 
smain constant but varies inversely as the cross sectional area of 
le passageway. 
fThe path described by a particle of water in passing through the 




Fig. 205. 

ivhcel has been investigated by Francis,* by a method based upon 
the assumption that "every particle of water contained in the 
irhecl, situated at the same distance from the axis, moves in the 
«ame direction relative to the radius and with the same velocity." 
This assumption becomes more accurate as the number of buckets 
increases. 

Fig. 205 shows the path, resulting from the application of this 
assumption, of the water through the "Tremont" Fourneyron wheel 
and Fig. 206, through the center vent wheel at the Boott Cotton 
Mills. The former indicates, since the jet of water is carried for- 
ward in the direction of rotation, that the water resists the rota- 




Plg. 206. 



•See "Lowell Hydraulic Experiments," p. 39. 



3iS 



Hydraulics o£ the Turbine. 




Fig. 207. 



tion of the wheel until nearly to the circumference when it is sud* 
denly deflected and leaves the wheel, as it should, in a direction 
nearly normal to the wheel. 

The jet of water in the Boott wheel (Fig, 206), on the other 
handf shows a continual backward deflection of its path from the 

point where it leaves the guideSt and 
hence a continual delivery of tb 
energy to the wheel This seems to 
indicate a more logical conditioaand 
a better shaped bucket than that of 
the Fourneyron, It will be noted 
that the actual path of the water in 
this case is very similar to that in the 
impulse wheel shown in Fig. 204. 

For the economical operation of 
the reaction wheel the following 
principles must be observed; 
1st. In order that the jet of water may enter the wheel without 
shock the resultant of the velocity of the water as it leaves iht 
guides and the velocity of the periphery of the runner must have 
a direction parallel to the bucket blades at this point, and a mag* 
nitude equal to that which will produce the required discharge 
through the cross sectional area of the passageway. 

2nd, The relative velocity of the bucket and of the water relative 
to the bucket at the point of discharge must be such that the water 
leaves the buckets with the minimum practicable absolute velociiy^j 
3rd, Such residual velocity as may remain in the discharging wi 
ter must be conserved and utilized as far as practicable by tb 
proper arrangement of the draft tube. 

4th. In all wheels it is also essential by proper design to re^iuO 
losses from friction, eddying, etc., as greatly as possible. 

The first requirement is illustrated in Fig. 207 where AD is oft 
of the runner buckets of an outward flow wheeK The guides, AC 
direct the water into the buckets with an absolute velocity, v** 
velocity of the runner at point A, where the water enters, is u| 
The two velocities combined graphically give a resultant » v^ 
must be tangent to the curve of the bucket and eqtial to 



(18) 



T^^ — where 



q, = required diieharge throuj^h the pa^^agewftyi n&d 

«, = area of cniaa section of the paseageway at point of etitmiice. K 



Reaction WheeL 



3^9 



This reqtiirement does not enter into the desi^ of an impulse 
wheel since the jet impinges against the edge of the wedge-shaped 
partition in the bucket always in a direction tangent to the bucket 
curve at that point regardless of the relative speeds of runner and 
jet. Further, since the discharge is "free" and the buckets not 
'^filled/' no sudden change of velocity occurs. 

The effect of part gate conditions upon the first requirement de- 
pends upon the type of speed gate and may best be studied from 
Figs. i88, 191, 193 and 207. A change in either direction or mag- 
nitude of v^ will change Vr unless the two effects tend to neutralize 
which may happen in some instances. In all reaction wheels the 
velocity of inflow, Vi, through the guides is increased by partly 
closing the gate, while the velocity, ui, of the wheel remain un- 
changed, v^ will therefore change, and a change in either its direc- 
tion or magnitude will produce an impact or sudden enlargement 
respectively as the water enters the runner, and therefore a loss, 
unless the direction of the guides is changed to correspond. 

The wicket gate, when carefully designed, has given rise to part 
gate efficiencies more nearly approaching those of impulse wheels 
than with gates of any other type (see Figs. 131 and 236), 

Tlie second requirement, that of minimum residual velocity of 
the water in leaving the buckets, is shown graphically in Fig, 207. 
vm is the velocity of discharge of the water relative to the bucket 
and is, of course, tangent to the curve of the bucket, u, is the 
peripheral velocity of the runnen The resultant of two velocities 
is the absolute velocity with which the water is discharged from the 
wheel, and is shown in magnitude and direction by line v^. Now, at 
part gate the quantity of water discharged is less than that at full 
gate and hence vb must also be less since the cross section of the 
passage must be filled. Ua remains unchanged and hence the resul- 
tant Vj will be increased with a corresponding waste of energy and 
loss in efficiency. This is an unavoidable loss in a wheel operating 
under part load and makes it impossible to maintain full efficiency of 
operation by any design whatever of the regulating gates. This 
loss does not appear in the impulse wheel since the velocity with 
which the water leaves the bucket is theoretically at least not in- 
fluenced by the quantity. 

The third requirement is pnrtially satisfied by gradually expand- 
ing the draft tube from the wheel to the point of discharge. This 
will recover only the component of the residual velocity in the axtat 





320 



Hydraulics of the Turbine, 



direction, ITie larger component of the residual velocity however 

tends to produce a rotation of the water column in the draft tube, 

and is not recovered by any present design. 

The fourth requirement is evident* 




Fl^ 208-209.— Reaction ^Wlieel wttli Concrete Draft Tut)®.* 



TOTAL AVAfLAflLt ENCftCT 



"^«^^SE^ 




LC^ IM WHi:CL a'iS 



imUSCO Vr WHCCL-Kd 



VELOCITICS m DRAfT TUBE^ 



aciTy-QTT~Bi 



QSB liH VeiuQCITV-aTl fclflfel 



CHTRAWCE^ IMJCS 



DRAT* TUBF 



Fig, 210.— Graphical Relation of Velocity and Energy la tha Flow ThroQ] 
a Beactlon Turbtne wlUi Draft Tube. 
* Turbiaen and Turbinenanlagen, Viktor Gelpk^> page 61. 



Energy Transformation, Reaction Turbine. 321 

155. Graphical Relation of Energy and Velocity in Reaction Tur- 
bine—The relations of the changes in velocity and in energy in the 
passagne of water through a reaction turbine and its draft tube are 
graphically shown in Fig. 21a 

Fig. 208 shows the cross section of a radial inward flow reaction 
turbine with a concrete draft tube. The cross sections of the draft 
\ tubes at various points are shown in Fig. 209 from which it will 
be seen that the draft tube of this turbine gradually changes form 
and increases in cross section in order that the velocity of flow may 
be gradually decreased from the point of discharge of the turbine 
to the end of the draft tube. 

The changes in absolute velocity in the passage of water into and 
through the turbine and draft tube are shown by line V, V^, Vj, V4, 
VjI the height of the ordinates at these points shows the approxi- 
mate absolute velocities at such points in the flow. The absolute 
velocity is a maximum at or near the point where the water enters 
the runner and is decreased as greatly as possible at the point of 
its discharge into the draft tube. By gradually increasing the area 
^ of the draft tube, an additional reduction in velocity is obtained, 
the water finally issuing with a velocity Vg. The maximum veloc- 
ity, measured by the ordinate Vg, is, in reaction wheels, consider- 
ably below the spouting velocity (v^2gh). 

In its flow through the wheel, the velocity of the water relative 
to the bucket increases and becomes a maximum at the outlet of 
the wheel. This increase in relative velocity is shown by the line 
; v., v.. 

The energy transformation which takes place during the change 
in velocity is illustrated by the ooited line marked "Energy trans- 
[ formation" which begins at a maximum of 100 per cent, at the en- 
f trance of the wheel ; is decreased by friction, leakage, shocks, etc., 
I by about 16 per cent, under full gate conditions. The energy is 
! transformed into useful work in the wheel by the reaction at the 
[ point of discharge and utilizes about 80 per cent, of such energy, 
the remaining 4 per cent, being rejected in the discharge from the 
draft tube with a slight recovery of velocity energy as before de- 
scribed. 

156. Turbine Relations. — In all water wheels the quantity of dis- 
^arge, the power, speed, efficiency and effective head on the wheel 
^re closely related and vary in accordance with certain definite laws 
modified by the design of the turbine and the conditions under 



3Z2 



Hydraulics of the Turbine, 



which it is operated. The conditions of operation must be adapted 
to the type of machinery used, or the machinery must be selected In 
accordance with the conditions under which it must operate, in or- 
der that the best results may be attained. 

If a jet or stream of water, with a velocity, v, acts on the movinf 
surface of a motor bucket, this bucket, if the friction of the wheel is 
negligible, may acquire a velocity essentially equal to that of the 
jet, i. e., to the theoretical velocity due to the head. In actual prac- 
tice the velocity of the bucket will always be less by the amoum oi 
velocity lost in overcoming the friction of the wheel. The velocity 
of the wheel here considered mtist be measured at the center of ajh 
plication of the forces, i. e„ at the point of application of the result- 
ant of all the forces of all the filaments of water that act on the 
wheeL Under conditions where the resultant velocity of water and 
bucket are the same, it is evident that the water will produce no 
pressure cm the bucket and the motor can deliver no power* As 
soon as resistance occurs, the speed of the wheel is reduced. Under 
reduced speed the momentum of the jet, or the reactive pressure of 
the water, according to the circumstances of design, is converted 
into power. This impact or pressure increases as the speed or ve* 
locity of the bucket decreases until the maximum impact or pres- 
sure results with the bucket at rest, in which case also no work is 
done. At some speedy therefore, between these extremes the maxi- 




Turbine Relations. 



323 




aV3H lOOi N33X(ilHX (l3QNn H2MD6 aSMOH 




324 Hydraulics of the Turbine, ^^^H 

mum amount of work, from a given motor, will be obtained. That 
is to say, — at a certain fixed speed the maximum w^ork and the maxi- 
mum efficiency of a given wheel will be obtained, and at any speed 
below or above this speed, the po%ver and efficiency of the whd 
will be reduced. These conditions vary considerably according 10 
the type and design of the wheel considered and also according to 
the gate opening at which the wheel may be operated. 

The efficiency curves of a 48" Victor turbine, under a thirteen 
foot head and under various conditions of gate, arc shown in Fig, 
211. Fig- 212 shows the i^-power curve of the same wheel under 
the same conditions of head and gates. 

157* Relation of Turbine Speed to Diameter and Head.— Tlie 
velocity of the periphery of the impeller or buckets of a wheel is 
not necessarily and in fact is not usually the same as the velocity oi 
the point of application of the resultant of the forces applied to tlie 
wheel. This point may be at some considerable distance within the 
wheel and at a point not easily determined. This point of applica- 
tion of the resultant forces may vary in position with the gate open- 
ing. The peripheral diameter is fixed and is therefore more conve- 
nient for consideration than the point of application of the forces. 
The peripheral diameter^ or the catalogued diameter, is therefore 
used in the discussion of the general subject. Many w^hecls var}^ in 
diameter at various points on the periphery (see Fig, 174), and thertJ 
is no uniform practice among manufacturers in designating such fr 
ameters so that the diameters used in the following discussion ami 
the functions based thereon are in accordance with the practice oi 
each maker and arc therefore not strictly comparative. In this dis- 
cussion the laws discussed are equally true if based on any actual 
diameter or any simple function of the same. The diameter chosen 
simply influences the magfnitude of the derived function and not tk 
character. The discussion holds therefore in each case regardless of 
the method of measurement except for the purpose of comparison* 
between wheels of various makers in which case similar diameters 
must be used. 

In reaction wheels^ the buckets extend from the periphery of the 
wheel to a point quite near the axis of revolution (see Fig. ij8, 
Diagram I). In such wheels the resultant of the forces applied falls 
a considerable distance within the circumference of the wheel. In 
such wheels the peripheral velocity may exceed the velocity of the 
jet acting on the wheel. In impulse wheels (see Fig. 129, Diagram 
E) the buckets are small in comparison to the wheel diameter and 



i 




Relation of Speed to Diameter and Head. 325 

are located at the periphery ; hence, in this class of wheels, the re- 
sultant of the forces applied lies at or near the periphery, and the 
peripheral velocity will be less than that of the jet acting on the 
wheel. 

Taking the velocity of the periphery of the wheel as a function 
of the velocity due to head, the relations may be expressed by the 
formula: 

(19) v' = *p}/2gh ^^^™ which 

V' _ v^ 



(20) fp = 



>^2gh 



The velocity of the periphery of the impeller may be expressed 
by the following formula : 

/2i\ V D ir n _ 8.1416 D n 

^^' ^ ~ 12 ± 60 "" 720 

Combining equations (20) and (21) it follows that: 

,^v 3.1416 Dn ^ . ^Dn 

(22) ^= 720 X 8.025 /r = '^^^ VK 

From this may also be written: 

(2R) n = y ^^ = 1841.6 (p Vh' 

^ ' .000543 D D 

As equation (22) is general, it follows that when <p is constant: 

Dn 

(24) . —7^ = 1841.6 ^ = A is constant. 

If h=i, this will reduce to: 

(25) D nj = 1841.6 <?> = A 

The catalogue speed, power and discharge of each series of 
vheels, as given in the catalogues of manufacturers, are usually 
>ased on the conditions of maximum efficiency and constant ^. 

From the above considerations it follows that in any homogen- 
ous series of wheels, that is in any series of wheels constructed on 
niform lines and with dimensions proportional, the wheels of the 
erics are designed to run at the same relative velocity, and there- 
>re 



326 



Hydraulics of the Turbine* 



That is to say: In any hmriogeneous series of turbines the pr^ 
diici of the ddameter of any wheel D, (md the number of revohiim^ 
n, divided by VjT ^ill be a constant A provided <^ rsmaim comiani. 

In investigating the values of A and ^ for various makes of 
wheels, as expressed by the data in the manufacturers* catalogues, 
it is found that these values vary somewhat for different wheels o( 
a series but are usually practically constant. It will be noted, 
however, from the efficiency speed curve, shown in Fig, 211, and 
the ^ power curve, shown in Fig, 212, that the speed, and ccmse- 
quently the values of <^ and A , may vary somewhat without materi- 
ally affecting the efficiency or power of the wheel* 

It should also be noted from Figs. 211 and 212 that if it is dt 
sired to secure the greatest efficiency and power at part gatet the 
values of and A for a given wheel must be reduced* Table 
XXVI gives the values of A and it for various American wheels, 
calculated from the catalogues of the manufacturers. 



TABLE XXVI. 
ShcwiTig Belation of Diameter and Speed of VariouM Amm<:^n Tu,H>inuworkvf^ 

under Qatalogtie Conditions. 
D n V' 

Vh 



i 



A = -?T= 



V=-= .000543^ 



i 



Manufactiurer. 



Eeaetion Wheda. 
X a Aloott & Son. , 



Alex&ndefi Brmdley d 
Dunninjf 

AmericftD Steel Dredge 
Works-,.. 

•Camden Water Wheel 
Workfl. ....,.,-.... 

Cbate Turbine Mfg, Co, 



ChristUna Machine 
Co.. 



Name of Wheel, 



Alcott'a Standard 
High Duty , 

AleoiVg Special High 
Doty.. 



Syracuie Turbine..-. 
Liitle Giant , 



United Stfttee Turbine 
*Ch ase * J on val Tiir - 

bine (regutar).^. 
*Ch aae - J on val Tur- 
bine (ipecial) 



Balanced Gate Tut- 
bine 



Min. Ma^* 



Min, 






1210 


1254 


.658 


1211 


1253 


.658 


1203 


1226 


.664 


1235 


14§2 


.071 


1S72 


1588 


,745 


1612 


1907 


.876 


1840 


2337 


.099 


1220 


12d8 


.663 



•NoTK.— Wide Tarbtioo lo consUtiU due to the detfgfi beln|r 
(•ertCA not exactly boma^Qeoui}. 



.68! j 

.633 

M 

i.su 



■peoiil ftEir ?artoi» ilwd vbick 



J 



Relation of Speed to Diameter and Head. 



327 



TABLE XXVI— Continued 

SeUxHon of Diameter and Speed of Variotu American Turbines working 
under Catalogue Conditions. 






v' D n 

<p = l-=. 000543 -7== 
V Vh 



afacturer. 



Name of Wheel. 



Min. Max 



Min. 



Max. 



^ Wheel— Coiu 
dgway A Son 
dgway A Son 



!}lobe Iron 
Co 



LB. Dix. 



) Turbine A 

MUlCo 

) Turbine A 

Mill Co 

t Machine Co 

-ey Machine 



Hani Ma- 
Co 



need; Sons Co. 
efieldb Co.. 



Bros. Co. 



Doable Perfection . . . 
Standard 



American Turbine... 

fNew American Tur- 
bine (high head 
type) 

Improved New Amer- 
ican 

Special New American 

Improved Jonval Tur 
bine 



Flenniken Turbine.. 

McCormick'B Holyoke 

Turbine 

Hercules Turbine.. 



JIXL Turbine... 
tXLCR Turbine. 



McCormick Holyoke 
Turbine 

Hunt McCormick Tur- 
bine. 

New Pattern Hunt 
Turbine 

Standard Wheel, 1887 
Pattern 

Crocker Wheel — 

Samson Water Wheel 

Improved Samson. . 

Standard 

Special 

Phoenix ''Little 
Giant" 



1186 
1200 
1218 

1064 

16:^2 
1284 

1474 

1511 



1196 
1160 

1198 
1196 



1169 

1158 

1163 

1200 
1208 
1543 
1578 
1330 
1380 

1001 



1250 
1275 
1295 

1077 

1738 
1340 

1617 

1533 



1296 
1170 

1209 
1206 



1278 

1272 

1415 

1291 
1292 
1554 
1632 
1339 
1434 

1020 



.644 
.652 
.662 

.578 

.886 
.697 

.800 

.821 



.650 
.630 

.652 
.652 



.630 

.629 

.632 

.651 
.657 
.838 
.856 
.722 
.750 

.544 



.679 



.704 



.585 

.944 
.727 

.880 



.704 
.636 

.657 
.666 



.694 

.691 

.768 

.701 
.702 
.844 
.886 
.727 
.779 

.654 



nie reoommendf a maximum and minimum speed. Constants glTen are for the arer. 

baaed od full theoretical power of the water. Wheels are said to giwe from 75 per cent 
Mit effldeDcy, depending on location. 



3^8 



Hydraulics of the Turbine. 



TABLE XXVL^Continued. 

Showing Eelution of Diameter and Speed of Various American Turbintt 
tcorkmg under Catalogue Conditionsu, 






g> — 






= .000543 ^^ 



Mantifactarer. 



Beuction Wittel—Con. 

Nonish, Burn ham & 

Qo,,. 

Plait Iron Works Co, 



Poole Engineering ^ 

Machine Co^ 

T. H- HiadojKfeCo.,. 



8. Morgan Smith Co* 



Trump Mfg. Co., 

Wellman^ iSeaverj 

Morgan Co 



ImpitlBe WheeU. 

DeKemer Water 
Wheel Co 



Abner Dable Co 

Pelton Water Wheel 

Co., 

Plfltl Iron Worka Co,. 
The Riadon Iron Wks 



Name of Wlieel. 



Victor Register Gate 

Victor Standard CyJ- 

iTider Gat«^ .«..*. 



Poole- Leffel 

RiFdon Standard * , , 
Riadon Turbine Tvpe 

T, C. , 

Riadon Turbine Type 

a C..*.-. 

Smjth-McCorraick » 

Smith 

Standard Trump. - * 



McCormick.. 



DeRetuer Water 

Wheel .,. 

Tangential Wheel . * . 



Tangen ti II I Wheel., 
Victor High Press u re 
Tangential Wheel .... 



Min. 



1213 
1181 

1380 

1341 
1213 

12X3 

1213 
11 «0 
1656 
1320 

1212 



962 
a41 

912 

915 
917 



Ma3£, 



1233 

mi 

1410 

1380 
1420 

1420 

1420 
1344 
1679 
1380 

1260 



1001 
S4S 



919 



9 



Mill. 



,659 
.ti41 

.749 

-72S 
.659 

.659 

.(HI 

.898 
.716 

.658 



,522 
.456 

,495 

.497 
.49^ 



Mil. 



.670 
M 

J65 

.74& 

.77t 

,730 
.911 
.74ft 



I 






.S4^ 
.499 



i 




From equation (26) may be derived 

^1^1 /h" 

From this equation the economical speed or correct number of 
revolutions n for any wheel of diameter D» at any head, vX, cao 
be obtained if the revolutions n^ of any other wheel of the series 
at head h^ and of diameter Dj is known- 




Relations of and Efficiency. 329 

If in equation {2'j), D=Di, the equation reduces to 

That is to say r The ecciiomical speed of any wheel will he in direct 
proportion to the square root of the head uii\der which it acts. 
If in the equation (28), n — 1, the equation reduces to 
(39) n = nii/h 

From which it follows that the revolutions of a wheel (n) for any 
head, h, is equal to the evolutions nj for one foot head multiplied 
by^hT 

158. Graphical Expression of Speed Relations. — ^The relation 
expressed by equations 18 to 2^^ inclusive, between the values of v, 
<^, D, n, and h, are graphically shown by Fig. 213. The theoretical 
relations between V and h, and <^ as expressed by equatio'n (19) 
when ^=1, are represented by the upper curved line in the diagram 
referred to ordinates and abcissas. The relation between ^, v and h, 
where 4> has a fractional value or is less than 100 per cent., as is the 
case for all wheels working under practical conditions, is shown by 
reference to the curved lines below ; the fractional value of ^ as rep- 
resented by each line is given thereon. The relations between v, D 
and n are shown by the relations of the straight lines originating 
near the lower right-hand corner of the diagram referred ta ordi- 
nates and abcissas, and the mutual relations of all lines on the dia- 
grams show the mutual relations between the various factors that 
are here considered. 

159. Relations of (^ and Efficiency. — In any turbine running 
under different heads but otherwise under the same physical condi- 
tions as to gate opening, setting, draft tubes, etc., the efficiency will 
remain constant provided the ratio of the velocity of rotation to the 
theoretical spouting velocity of the water under the given head 
remains the same. This is to say, — the efficiency of a wheel will 
remain cottistant under various conditions of head as long as the 
value of <^ remains constant. This law is well demonstrated by ex- 
periments made on a 12^^ Morgan-Smith wheel at the Hydraulic 
Laboratory of the University of Wisconsin.* These experiments 
were made under seven different heads varying from about 7.10 feet 
to about 4.25 feet. The results of all these experiments have been 

*"Te8t of a Twelye-Inch McOormick Turbine/' an unpublished thoBis by 
O. W. IClddleton and J. C. Whelan. 
20 



330 



Hydraulics of the Turbin*^, 



ttiAe ii peer 




I 



REVOLUTlDltS PER MtNUTE 

Fis 213. — Speed Relations of the Turbloeei. 



Relations of and Efficiency. 



331 




0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 I.I 
VALUES OF (t) 

Fig. 214. — ^Efficiency— ^ Curve of a 12 "Smith-McCormick Turbine. 



332 



Hydraulics ol the Turbine* 



platted in a single diagram (see Fig. 214) from which it will be 
noted that all experiments are fairly cloee to the mean curve; that 
the variation therefrom is probably due to experimental errors 
(principally, it is believed, in the determmation of the relative 
velocities) and that reduction in head shows no uniform decrease 
in efficiency. The experiments referred to, which are soon to ht 
published in a University bulletin, show that this law is true under 
all conditions of gate as well as for the full gate conditions, illus- 
trated in Fig, 214* Hence the conclusion may be drawn that the 
efficiency of a wheel will remain essentially constant if <^ remains 
constant at least under moderate changes in head. 

160. Discharge of a Turbine at Fixed Gate Opening. — ^The dis- 
charge of a turbine with fixed gate opening, but at various speeds, 
is not always the same but varies within certain limits and as the 
speed varies. In some cases the discharge of a wheel increases as 
the speed increases. (See discharge of Tremont turbine, Fig* 215.} 
Sometimes the discharge decreases as the speed increases (sec disr_ 
charge of Victor and McCormick turbines. Fig. 215), and some 
times the discharge increases with the speed to a certain point ani 
then decreases with a further increase in the speed (see discharges 
Samson and New American wheels. Fig, 2I5<) 

In reaction turbines the discharge takes place first through the 
guide from which it passes into and through the buckets of the: 
wheel The relations of these two sets of orifices change as thij 
speed of the wheel changes and affects the total discharge. If i^4 

ing such changes of speed, the ratio, i^= — , remains constant,*^ 
is found by experiment that the conditions remain similar to thos-^ 
of any short tube or orifice. The discharge of a turbine may then 
fore be determined by the formula ; 

(30) q = i^Vlgh 

And it may be stated: In a given turbine with Hxed gate opi^ 
the discharge nnU be proportional to the square root of the 
I. e., the dischaff^e ditnded by ■/JT is constant 

The values of C and a vary with the opening of the gate orpt< 
but for any one position are essentially constant. 

Let the discharge of a wheel under fixed gate conditions andwitS 
a given head, h,j be given by the formula; 
(3i: q, = Ca/2gh7 



k 



Discharge of a Turbine at Fixed Gate Opening. 



333 



The discharge o£ any other head will be proportional to vT" and 
therefore 



(32) 



hence 



(33) 



q = 



qiVTT 



or if hj = 1 



(84) q = q,i/F 

Therefore, it may be stated: In a given turbine with fixed gate 
opening the discharge at any head h wiU be equal to the discharge at 
one foot head multiplied by y/h. 

That this law is essentially correct may be demonstrated by ex- 
perimenL Fig. 216 shows the results from the series of tests on 
the McCormick turbine, before mentioned, at full gate. Tljree sets 

110 



100 



80 





Sao 

3 
J 

i 



70 



BO 



SO 















\ 




< 


^ 


1 
> \. 






\ 




1 


\ 






\ 


I 

6 




i 


V 




\ 




A- 4 8'' VICTOR CYLINDRICAL CATE 
B-SS^'tURBINE LOWELL mass 




! 


I 


U" ^^ llWIr 

D- 4S''8AK 
E-5|"M£( 


ASON 
;ORMICK W-l 


l-MORBAN 



2S 



30 38 40 4S 5 

0IBCHAII6E IN CUBIC FEET PER 8BC0N0 UNDER ONE FOOT HEAR 



95 



Fig. 215. — Full (3ate ^-Discharge Curves of Various Tarbinefl. 



^m 334 Hydraulics of the Turbine* ■ 

^1 of experiments are platted with values of 4> equal to .35, ,65 and .90 
^M and for heads from about 4.25 feet to 7.1 feet. Fig, 217 shows the 
^M discharge of this turbine at various gate openings and under seven 
^M different heads. For the purpose of this diagram the discharge*^ 
^m under each head have been reduced to the theoretical discharge at 
^M one foot head by equation 34. It wHt be noted from both Fig, 2t6 
^m and Fig. 217 that all experiments where i^ is the same lie close to 
^1 the average line, and that the departures from this line are prob- 
^M ably due to experimental errors. The results are sufficiently close, 
^M however, to demonstrate that the discharge under practical condi- 
^B tions essentially follows the law above expressed. j 


y 

1 4 

a 
y 

i 

1 


























i 


f 


/ 


/ 






« 


























h 


/ 


























< 


1 


i 


/ 


























/ 




h 


i 


























I 


/ 


/ 


























/ 


f 


u 




























/ 


/) 


/ 




























/ 


/ 


y 






























V 


r 










mL 




















fe> 












1 
















/ 


A 


r 


) 












1 














/ 


A 


y 
















% 












J 


Oa 


'/ 


















1 










/ 


9^ 


r 




















I 








.€^ 


^ 


^ 






















1 




0^^ 


^ 


'^ 


























1 


k 



216 


1 t 3 4 I i ? 1 

DISGHAHCC IN CUBIC FZZT FCH SEtQNO 

—The RelaUQQi of Head to Discharge of a 12 "Smitli M^Corml: 

Turbine. 


>^| 



Discharge of a Turbine at Fixed Gate Opening. 



335 



i6i. Power of a Turbine. — ^The power which may be generated 
by any wheel depends on the head a mailable, the quantity of water 
which may be discharged through the wheel under the given head, 
the relative speed at which it may be run, and the efficiency of 
operation. Hence 



(35) 



p _ q w h e _ q he 
560 "" 8.8 



Combining equations (30) and (35) there results 
(86 > p _ Caw l/2i h*e _ Cai/2g h^e 



550 



8.8 



From equation (36) it is apparent that if C, e and a are constant 
for any given turbine and fixed gate opening, and if the value of «f> 
remains constant, the power of the turbine will be in direct propor- 
tion to h*. consequently 



1.1 


07 














i 




s 


% 


\ 


















( 1 














*\l 






^ 


fr* 


^ 


























\ 






^ 


V 


^ 


> 


53- 












iJ 

# 

i" 












a 


t 






\ 


t 




^. 


d 


















( 


't i 












v^ 








^ 


<l 




# 




















«*\| 












^^ 












■ 


Ns 
































* 










;> ' 




• 


K, 








t».i 






































Lli 








1 








m 






















< 


^*Y 




1 


L 






Q 1.1 




1 








u" 






















tk 1 






% 








« 










^r 
















[ 










> 




^i 


h 




gM 
Lt 


( 


1 










• 






















■ 1 


I 




■ 


\a 












M 














( 










Cfa 


03 






\ 




^ 
























^ 
















m 






f 


































1 1 






n 


, 


1 
< 


i 








^ 


f 
























^' 






















ft 






















^ 


^ 








i 


( 


» 






















_1 










' r 


> 






• 
















4 




















/ 













e,r 














& 1 


— 


— 




— 


— 


s 


















S\ 


i 






















iif- 
3 










g<i 


u 


iJ 




















^ 










LIl 






__ 



1*1 1.0 a*i 

FKT rai.NBOND UNOOI ONE FOVT HCAO 



Tig. 217.— Helatlons of Velocity to Discharge for a 12* "Smith-McConnlbk" 
Turbine at Various Gate OpeDlngs. 



336 



Hydraulics of the Turbine. 



ir) 



P P. 
h» - hi 
Equation (37) may be reduced to 

P,hl 



(88) 



P = 



hj 



x^'rom which can be determined the power of a wheel at any given 
head, provided its power at any other head is known. 
In equation (38) if hi = i, there results 

(39) P = Pih» 

From which it may be stated : In a given turbine with a fixed gait 
opening, the power that can be developed' at any head will be equal 
to the power at one foot head multiplied by h^. 

This law may also be demonstrated experimentally as will be 
seen by reference to Fig. 218, in which is shown the theoretical 
curve representing the relation between head and horse power of 
the 12" McCormick turbine before mentioned. The turbine on 
which these experiments were made was small and the heads were 



Z 4 

a 

























> 


^ 










^ 


/ 






















» 


^ 




■ 






. ,_^ 


4^ 


^ 






















< 


y 








m^ \ 


^ 


X 




^ 


^ 


















/ 


/ 






c 


?r. 


^ 


^ 


i^' 




















y 








^ 


y^ 


\ 
























/ 


/ 






y 


y 


^ 


y' 


n 






















y 


/ 




{< 


[y 


^ 


y 
























fl 


t 


/ 




/^ 




y 






























/ 




y 


<< 


r 






























/ 


vH 


<; 


y 
































/ 


y 


C' 


^ 
































/ 




y/ 


^ — ^ 


































u 


^ 




































/ 


r 






































/ 








































r 




































ii 



Q 1.0 a.o 9,0 ^ 

ACTUAL HORSE POWER OP WHEEL 

Fig. 218.— Relations of a Power to Head tn a 12 "Smlth-McCormlck Turbine." 



The Relation of Discharge to Diameter of a Turbine. 337 

limited so that there is some variation from the theoretical curves 
but the fact expressed by the general law is quite clearly shown. 

162. The Relation of Discharge to the Diameter of a Turbine. 
—In any homogeneous system of water wheels, the diameter, height 
nd corresponding openings and passages are proportional and it 
ollows that in such similar wheels similar areas are proportional to 
ach other and to the squares of any lineal dimension. In such 
vheels, therefore, the area a of the gate openings is proportional to 
he square of the diameter of the wheel, and the equation may there- 
ore be written : 

(40) Oal/2i"= K D» 

In this equation K is a constant to be determined by experiment. 
Combining equations (40) and (30) there results 

(41) q = KDVF 

from which can be obtained, by transposition 



(42) 



D=4/ q 



Equation (41) is not only theoretically but is also practically cor- 
ect, as is shown by the data in Table XXVII, which is also graphi- 
:ally represented in Fig. ^19. These data are taken from a paper 

TABLE XXVII. 
Discharge of thirteen water wheels of the same manufacture but of different di- 
ameters, €u determined by actual tests, compared with value computed by the 
formula: 

q = K D* •? Id which h = 13, K = .0172 
DISCHARGE. 



No. 


Diam- 
eter in 
inches. 


Redaced 

from actual 

teste, Cu. ft. 

per Sec. 


Computed 

(Mean 
Curve) Cu. 
ft. per Sec. 


Variation 
from Com- 
puted Dis- 
charge Cu. 
ft. per Sec. 


Per cent. 
Variation 
from Com- 
puted Dis- 
charge. 


1 

2... 

3.... 


9 
12 
15 
18 
12 
24 
27 
30 
36 
39 
42 
45 
61 


5.17 

8.79 

13.85 

18.85 

29.07 

35.31 

47.81 

54.15 

77.33 

93.51 

107.73 

128.53 

161.07 


6.02 

8.92 

13.93 

20.07 

27.32 

35.68 

46.16 

55.75 

80.28 

94.22 

109.27 

126.44 

161.12 


+ 0.16 
-0.13 
-0.08 
-1.22 
+ 1.76 
-0.37 
+ 2.65 
-1.60 
—2.95 
—0.71 
—1.54 
+ 3.09 
-0.05 


+ 2.99 
—1.46 
-0.57 
-6.08 
+ 6.41 

1 04 


A 


5.... 


6.... 




+5.87 
—2 87 


^■.. 


9.... 

lo "";• 


-3.67 
—0 75 


ll : ; 


— 1.41 


12, 


+ 3 10 


13. . . 


— o.o.s 







338 



Hydra uiics of ihe Turbine. 



by A, W, Hunkin^, entitled "Notes on Water Power Equipment/' 
in vol. 13, No, 4, of Jour. Asso. Eng. Soc, April, i894* In this tabic 
are given the discharges of thirteen water wheels of various diam- 
eters, the discharges of which were determined from actual tests. 



DIQCHAIiar IN CUBIC FCCT Kfl SCCOND 



55 

1 



S 



S fi I 


5 ; 


3 C 


« 4 
3 C 


^ □ D 


4 




















H 




















^ 




^s 






















vi 


^ 


Sv^'^s^ 






















° 


^ 


°^ 


br-^ 






















*'^a 


? 







Fig, 219. — Relations of Dlacharse to Dtameter in EeacUon TiLfblAt of tie 

sama manufacture. 

These results have been reduced to the common basis of the dis- 
charge at 13 foot head. The computed discharges at 13 foot heati 
on the basis of equation (41) are also given, as well as the percent- 
age of variations of the actual from the theoretical discharges. The J 
wheels were of the same make with inward and downward di*- m 
charge. The departures or variations from the mean values, as d^ 
termined by calculation, are probably due both to imperfections l^ 
the construction of the wheel and to errors in making the tesEs. 
They may be seen, however, to practically conform to the theoretT 
cal deductions* The values of the coefficient K, as calculated froru , 
the tables contained in the catalogues of various manufacturers cf 
American wheels, are given in Table XXVTII. 

163, The Relation of Power to the Diameter of a Turbine.— Bf 
substituting the value of q from equation (41) in equatioa 

(SS) "-"'"' 

there results 

(4S) P = 



i 



aB 



D»h*Ke 



S.S 



"(S)"-' 



The Relation of Power to the Diameter of a Turbine. 339 



TABLE XXVIII. 
'mg Belatum of Diameter and Dieeharge of Varioiu American TurMnea 
working under Catalogue Conditions, 

_q 



K = 



D'l/F 



M&nuiactuTer> 



Name of Whe«l, 



Min, 



Max. 



Meaetion Wh^el^ 

41eoUd 80a 

odtr^ Bradley & Dunn 

icmn Ste«l Dredge Wki. 
en Water Wheel Works 
Turbine Mfg. Co 

iana 3Iachine Co. ... . 

Bidgway & Son Co,. » 

Eidgway 6l Son Co.. . 

\n Globe Iron Worka O 



fcS, B. Dix. 

lue Turbine & BoUt* 

[ Co , 

loe Turbine & Rolle 
rco 

}ke Machine Co. ....>. 
>hrey Machine Co. . . . 

ej Hunt Machine Co. 



Jones ^ Sons Co., 
) Leffel (k Go. 

on BroB. Co , ., 

ih, Btimham A Co. 
Iron Works Co*... 



AlcoU'e Standard High Duty 
AleoU'a Special High Duty . 

*9yracuee Turbine - - . 

^Little Giant...* «. ...i .... 

United Slatea Turbine. 

*Cba9e-Jonval Turbine ( reg- 
ular).. p ,,. 

•Chaee-Jonval Turbine 
(apecial). .,.. .«. .. 

Balanced Gate Turbine 

Double PeriecUon 

i?tandard ***,** 

'American Turbine 

New American (high head 
^vpe) 

Improved New A^leri(^an.. 

Speciitl New American 

Improved Jonval Turbine.. 

Flenniken Turbine 

MeCormickVfl Hoi yoke Tur- 
bine. , 

Herculea Turbine 

tlXL Turbine 

fXLCR Turbine..*, 

McCormick^B Holyoke Tur- 
bine. ............... . * , 

* H u n t- McCorm iek Tn rb i n e . 

New Pattern Hunt Turbine. 

Standard Wheel, 1387 pat- 
tern 

Crocker Wheel 

Samaon ,,,,., 

Improved Saoison. 

Standard 

Special ..*..., ... 

iPboenix "Little Giant". .. 

Victor Register Gate. 

Victor Standard Cvlinder 
Gate .' 



.00B54 


.00860 


,0157 


.0168 


0053S 


,00622 


0205 


.orMO 


02U 


.0229 


0064*3 


♦00913 


OID&O 


.01346 


00902 


.00052 


,0116 


.0142 


006S6 


.0005^ 


00543 


.00801 


00509 


.00644 


0233 


.0263 


0175 


.ti205 


00454 


.00546 


00052 


.01^ 


0184 


.0191 


0162 


.0176 


00361 


.0053& 


00645 


.00063 


01877 


.01929 


01913 


.02867 


01297 


.01643 


OIS.'J 


.OHI 


0175 


Min 


0170 


,0171 


022 


.022 


O116I2 


.00fi4a 


,00ft37 


.00966 


00924 


.0172 


.00917 


.00955. 


.0107 


.0186 



.0222 



.0327 



340 



Hydraulics of the Turbine- 



TABLE XXVIIL— Continued, 
Showing Bdaiion of Diameter and Discharge of Various American TvrMfut 
toorking under Catalogue Condiiiona, 





Name of Wheel. 


K 


aiannfactnrer. 


Min. 


Mu. 


Beactitm Wiieels. — Cod, 

PcK>le Kngineering and Ma- 
chine Co ..,,,- ^ ^ «,. 4 ♦ . . . 


Poole- Leffel .*•-,,,,. 

*Risdon i^iandard Turbine* * 
*Rifl(lon Type T. C Turbiae 
♦Risdon Type D. C, Turbine 

*Smith-McCormick 

Smith ..>>..* 


.00625 

.00501 

.00753 

,0100 

,0187 

.0247 

.0210 

.01&& 

.000185 

,mxx*75 
.00010 

.0017 
,000184 


1 

.OQ6S7 


T H* Riadon & Co 


.00398 


S. Morgan Smith Go , . ^ 


.01S2 

.0238 
.0256 


Trump Mfjf, Co. 


MiJiTid*Lwl Tmirm^ ^ - . « ^ 


.021)3 


Wei Im fin, Seaver^ Morgan Co. 

Impulse Wheels* 
D^Eeme^ Water Wheel Co. . 
Abner Doble Co .,.*.,. 


McCormick 

♦DeRemer Water Wheel. , . , 
^Tangential Wheel 


.om 

.00017S 

000 Hi 


Pelton Water Wheel Co. . - - . 


*Tangential Wheel . . , 


.000136 


Piatt Iron Works i_:o 

HiBdon Iron Works ...*■.,.., 


Victor HiRh Pressure 

*TanK«ntial Wheel , . 


,00247 
.000175 









*Wlrte varlmiioD tn oniniitaiaia ^ue to the d^aij^ btlng epecfAt for T^rioos alc^ whestH (ferim 
n>i pxar^tly hotrioifeu#<iu«i, 

tTaiiJes in caTAJo^ue bofad on fuU theoretical power of the wi(«r. Wheela are said lo fl*ft &tHn 
7£ per cent to 90 per cent ifffleieDv7i depend Inf? on location. 

|Mun»c>a Bros. Co, rnnke Mver&Jtypea of "LUte Qiaol** turhJn«« c&tufaff t,borit wide tafi»ttDQ li 
^ ^nstftjilfi. 



Asf --^1 is constant for a given wheel, as lon^ as ^ is constant, 

thj.s expression may be represented by a constant IQ which may 

be derived independently for each make of wheel, or may be deter- 
mined from the equation 



r («) 






With this 


substitution 


(43) 


becomes 


(45) 




P = 


= K,D«h* 



IL Til at is to say: With zv It eels of homogeneous design, the pawif of 

H any uheel under the given head is in direct proportion to the sqmre 

H of its diameter. This law ts both theoretically and practically cor 

H rect, as demonstrated by Table XXIX, and Fig. 220, taken from tlie 

H pnper by Mr, H unking to which reference has previously been 




Relation of Speed to Discharge of Turbine. 



34^ 



TABLE XXIX 

Rone Power of ihiriem water wkeeh of the mme manufactitre hut of diferent 
diameiers, as determined 6y actiuil te^tif compared with values determined 
by thjs formula: 



P=K, D' 



K, ^.00158 
HORSE POWER 



h = 13 



Ha 


teriu 
inches. 


FromTeatfl. 


Computed. 


VarUtioti 
from Com- 
puted H. P. 
inH.P, 


Variation 

from Com- 

pated H. P. 

Percent. 


1 .,.„..*. 

2 


9 
12 

15 

18 

21 

24 

27 , 

30 

36 

39 

42 

45 

51 


aio 

10.41 

16.49 

22.89 

S3. 71 

41.53 

66.67 

63.69 

97.45 

109.98 

133.09 

15:1,82 

190.28 


6.00 

10.67 

16.67 

24.00 

32.67 

42.67 

54.07 

66.68 

96.a) 

112,68 

130.69 

150.02 

192.69 


+ 0.10 , 
^-0.26 
--0.18 
-1.11 
+ 1.04 
—1.14 
+ 2.60 
—2.90 
+ 1.45 
-2.70 
+ 2.40 
+ 3.80 
+8.59 


+ 1.67 
—2.44 


4 1 


—1.08 
-4-62 


5,, 


+ 3.18 


e.. .*,..--.. 


-2.67 


7 


+ 4.81 


8 


-4.48 


9 ,. 


+ 1.50 


10..,.. ,. 


—2.40 


u ., 


+ 1.84 


12 


+ 2,53 


13 


+ L86 







t 


n 

3 C 


HOMk. MWCn 

isssiiiissi 


o 


* 






















2 ° 


\ 


^. 






















K 


h 


"^^ 

"W '^j' 
















X o 

9 *■ 








*Vk^< 


^ 


f^ 


^''0 *, 










i 














"•"--Is 


^ 


£!^ 


vja 





























_^Flg. 2:0. — Relation of Power to Diameter in Reaction Turbines ot tbe same 
■ manufacture. 



H 3^2 Hydraulics of the Turbine, ^^^^H 

H made. This table and figure illustrate the relation between the the- 
H oretkal power, as determined by equation (45), and the actual horse 
H power of thirteen wheels of the same manufacture but different 
H diameters, as determined by actual tests. 

H The values of the constant K^ for the most efficient relation of 
H power to diameter in various American turbines, as calculated from 
H the iables contained in the catalogues of various American manii- 
H facturers of turbines, are given in Table XXX, The values of K, 
H and other turbine constants will be found to vary widely in the 
H various types of turbines, not only of different manufacturers bur 
H of the same manufacturer. Tlie interpretation of this fact is not 
H that one turbine is, in the abstract and according to the relatii^T 
H value of the constants, more valuable than another, but that each 
H turbine is best fitted for a particular range of conditions for whicb 
H it was presumably designed, 

■ TABLE XXX. 

H Showing Bdation of Power and Diameter of Various American TurMn€$ Work 

^M ing under Catalogue Conditions^ 




D» h* 


1 


^p Manufacturer. 


Kame of Wheel. 


K, 


Min, 


Mai. 


K Reaction Wheela. 

H T. C. Ale ott & Soil .*»,. 


Alcott's Standard High Duty 
Alcott's Special High Duty. 

Syracu^^a Turbine<*«* •« .... 


.0005S9 
.00141 

.000483 

.oaiQO 

,00190 

.000590 

.000932 
.OCtOBOO 
.00113 
.00053S 
.0004S4 ! 

.000422 
.00212 
,00158 
.000447 

.000506 
.00167 


.mm 

.00155 

.mm 

,003St 

.00:20: 

,OO0M 

.001150 

,00150 
,00088 

.omB 

,00GS8* 
.0024* 

.00187 
.000652 

.oooiie 

00173 M 


^ Alexatidefp Bradley & Dunn- 


American Ste^l Dredge Wki, 
Camden Water Wheel Worki 
Cbaae Turbine Mfg. Ck». . . . . . 

ChriitianH Machine Co. . . . . , 

Craig, Hidgway ^k Son Go 

Craig, Ridgway & Son Co*. . . 
Dayton Globe Iron Works Co. 

J L AS B Dix *. 


Little Gmnt. 

United States Turbine 

*Chase-Jonval Turbine (reg- 
ular) ..,..-.,,,.^ 


*Che«e- Jo n va i Tu rbi ne 
(ppeclal) .,....,.. 


Balanced Gate Turbine. * . , . 
Double Perfection ..,.,,*,,. 


Standard ,.., .. ..,, » 


* American Turbine ....♦*., 

*New American ( high head 

type), ,*,,,.,......,,,,.. 


Improved New American,,, 
*Sp&cial New Amerii-an ..... 
Improved Jonvai Turbine*. 

Flenniken Turbine • «■■■«• * 


Dubuque Turbine Je Roller 
Mill Co.... ..-, .^ 


Dubuque Turbine *& Roller' 
Mili Go .1 


McCormick*s Hoi yoke Tur-i 
bine I • ^•,, ,i*.>>«*4< 




m 









The Relation of Power to the Diameter of a Turbine. 343 



TABLE XXX.— Continued. 

Showing Mdatitm of Power and Dianveter af Varwus American Turbinet Work* 
ing under Catalogue Conditions, 



K. = 



D* h5 



Manufacturer. 



H&tne of Wheel. 



I^eaction Wheel— Con, 

Hoi yoke Machine Co. 

Humphrey Machitie Co. . . 



Rodney Btmt Macbioe Co. . . 



E. D. Jonei A 0otii Co. 
James Leifel & Co 



Muti£on Btob, Co 

Norrisb, Bumham &Co. 
Piitt IfOD Worka Co 



Foole Engineering and Ma- 
chine Cix — *.,,,, 

r H, RifidonitCo 



S. Morgan Smith Co. 



The Tranrip Mfg. Co 

Wellmanj Seaver^ Morgan Co 

ImpuUe WheeU 

DeRemer Water Wheel Co 

Abner Doble Co 

Pehon Water Wheel Co. . . 

Piatt Iron Worka Co *. 

Riidon Iron Works Co. . . . 



Hercales Turbine 

tlXL Turbine »»*••»«. 

tXLCR Turbine 

McCormick Hoi yoke Tur- 

bine^. , '. 

*Hunl McCormick Turbine. 
New Pattern Hunt Turbine 
Standard Wheel, 1S87 Pat 

tern ,. 

Crocker Wheel 



Improved Samion, 

Standard ,-,>>.. 

HDCcial .<<* 
tPboenii'*'*LiUle Giunt'* . * ' 



Victor Keeister Gate 

Victor Standard Cylinder 
Gate 



PooIe-LeEfel 

*Rl9don Standard Turbine. 
•Rifidon Tvp© T. C Turbine 
♦Risdon TVpe D. C. Turbine 
Smith -McCormick *•*.,*< 

Smith ..,,.,,,. 

Standard Trump, 

McCormick.. 



*DeRemer Water WheeL . . 

♦Tangential Wheel , * 

*Tan^ritial Wheel , 

Victor High Preeeure. ,.,,,» 
•Tangential Wheel 



K, 



Mm, Max, 



.00147 

.000397 

.000730 

.00109 
.00173 
.00120 

.00101 

,00159 

.00158 

.00201 

.00056 

,000897 

.000842 

.000852 

.00158 

.00205 

.000026 

.000485 

,000672 

.000781 

.00169 

.00232 

.00191 

,00168 



.000124 

.0000065 

,0000095 

.000154 

.0000128 



.00159 
.000620 

.ooiaio 

.00173 
.00260 
.00146 

,00122 

,00163 

,00159 

,00202 

.Oft^S 

.000920 

.001560 

,000885 

,0017a 

,00206 

.000650 

.000675 

.000913 

.00135 

.00217 

.00236 

.00241 

.00171 



,000186 

.0000107 

.0000130 

.000523 

.0000165 



*Wtde T»rliLtlo«i In tsofoaJtmnU dti« to the deslfrn beln^ ipeclml far TarJoua mizod wheels (aerie* not 
rxmeG.1v hDmosviieoi.t*i. 

tT&bl«!« bM«d on full theoretical power of the wAter, Wheals mre said ta kItb froDi 7D per eeiit 
to m per cent «ffioieQcy, depend ja? od JocaUod. 

tlf uaimii Bro«. CCk tn&ke KTerai iypm of "Util» Gluit" turbf see, OttUiLog: ftbore wide variation 
in t 





344 



n 



CM 



UJ 



01 






m 



r 



n 



CM 



^ 



Hydraulics of the Turbinep 




ID kn 



TO CM — 



S^HQNJ m 123KM iO tilXinVIG 




Relation of Speed to Discharge of Turbine. 345 

c power of a wheel varies directly with the value of Kj, this 
t is a direct measure of comparative power and indicates 
tive power that can be developed by various types of wheels 
liameter and under a given head. The range of values for 
3und in American practice is shown graphically in Fig. 221 
he power of turbines of various diameter and types under 
t head is given. The power of a wheel varies under differ- 
ds as h', and therefore the power at any head can be de- 
d directly by multiplying the readings of the graphical table 
For example, from Fig. 221 it will be seen that various 
E 40" American wheels, under one foot head, will give from 
. H. P. and at 16 foot head they will therefore develop 64 
le H. P. at one foot head or from 48 to 256 H. P. within 
ange a choice must be made. 

Rdatiocis of Speed to Discharge of Turbines.— As the speed 
rheels of the same series must be proportional to Vh, the 
1 may be written : 

v/ = K. /F 
[lich and from equations (19) and (21) 

equations (42) and (47) may be derived 
„_ 12x60K,l/K "^ 

e first term of the last expression is constant, there may be 

^ 12X 60 Ka VK 
K. = . 

hich equation (48) may be re-written. 

head of one foot, b=si, equation (50) becomes 

ion (50) may be rearranged to read : 



Vh 
21 



^•=*»/*"^S 



346 



Hydraulics of the Turbine* 



TABLE XXXL 



Showing Relation of 5p^erf and IHmharge of Various Ammican T^^m 
Working under Catalogite CondUion^ 



Mftnufactnrer. 



Fame of WheeL 



£. 



Mid. 



Ecaction Wheeh. 



T. a AlcottA Son. 



Alexander, Bradley A Dunn 

ing.. 

American Steel Dredge Wrks. 
Camden Water Whml Works 
Chase Turbine M fg. Co . . > « 



I 



Cbnetiana Mscbine Co, . . « . . 
CrtLig, Bidgway d Son Co.,. . 

Gmig, Bid^way & Son Co 

I)ty ton Globe Iron Works Go, 



J. L. AS. B. Dii, ,.. 

Dabuque Turbine & Roller 
MillOi...,., 

Dubuque Turbine A Roller 
Mill Co. 



Holyoke Machine Co. 

Humphrey Macnine Co* ., 

Rodney Htuit Machine Co. 



E. D. Jones A Sons Co* 
Jamee Leifel & C£iv>,... 



Mnneon Bros. A Co. .. . 

Norrieb^ Burn ham A Co. 
Piatt Iron Works Co..., 




Alcott'fl Standard High Duty 
Aicott'a Special High Duly 

* Syracuse Turbi ne 

^Little (iiant i , . 

United States Turbine* **** 
*Chaae-Jonval Turbine (reg- 
ular) 

*Chage-JDnval Turbine 

(special). . 

Balanced Gate Turbine. * , 

Donble Perfection, ^ . 

Htandard 

* American Turbine ...... 

tNew American (high bead 

type) *^.<. 

Improved New American.*, 
Special New American* . » ♦ . 
Improved Jonval Turbine, . 



F^enniken Turbine. 



McCormick'fl Holyoke Tur- 
bine * .- • - 

HerctileB Turbine. . . . ^ . ^ ^ 

tlXL Turbine 

JXLCK Turbine. 

McCormick's Holyoke Tor* 

bine 

*Hunt McCormick Turbine 
*New Pattern Hunt Turbine 
Standard Wheel, 1^87 Pat- 
tern ., 

Cn)cker Wheel p 

Samiiion Water Wheel**** 

Improved Sam peon, 

Standard >* .**, 

Special ♦ * 

JtPhoenix *'Little Giant" 



« f .. t « - > ^ 



Victor Eeiriater Gat-e 
Victor Standard Cylinder 
Gate * * 



98. 8 
154.5 

89. S 
17^.0 
205. 2 

140. 

201.0 

115.8 

90.5 

04.0 

S3.0 

75.4 

265.0 

170.5 

84.0 

122.0 



162.0 

14S,0 

71.3 

90.5 

loSI.5 
161 .4 
132.4 

126.0 
161 .0 
201.7 
240.0 
103.7 
134/7 
102.0 
115.9 
153.0 

205.0 



Mai. 



mj 

243.1 

m>i 

174.0 

235.0 
156.2 
97.2 
lOli 
109.0 

85.9 

M*0 
190.0 
100 

mo 



17B.0 
1M.(^ 

tl6,fl 

ITfi.O 
207,5 
174,8 

m.o 

24 L3 
JOT .ft 

mi 

132.1 
1^.0 

212.0 



J 



Relation of Speed to Power of Turbine. 



347 



TABLE XXXI.— Continued 

howing Relation of Speed and Discharge of Various American Turbines 
Working under Catalogue Conditions^ 



'* = "^i 





Name of Wheel. 


K4 


Manufacturer. 


Min. 


Max. 


Reaction Wheels,— Con. 

*oole Engineering and Ma- 
chine CJo • 


Poole-Leffel 


110.4 
93.4 
100.7 
108.0 
163.7 
265.0 
194.0 
168.6 

11.10 

6.61 

9.21 

37.8 

10.67 


121.6 


'. H. Risdon A Co 


•Risdon Standard Turbine. . 
*Risdon Type T. C. Turbine 
♦Risdon Type D. C. Turbine 
Smith-McCormick 


117.2 


w Monrain Smith Co t - - 


137.3 
158.0 
185.0 




Smith 


266.0 


*he Tmmu Mfflr. Co 


Standard Trnmn 


190.0 


Wllman, Seaver, Morgan Co. 
Impulse Wheels, 

)eRemer Water Wheel Co. . 
Lbner Ooble Co 


McCormick •• 


179.0 


DeRemer Water Wheel 

*Tanffential Wheel 


13.20 
9.20 


^elton Water Wheel Co 


Tangential Wheel 


10.92 


*latt Iron Works Co 


Victor High Pressure 

Tanirential Wheel 


42.2 


tii>don Iron Works 


12.10 









*Wide variation in constants due to the design being special for various sized wheels (series not 
zsctlj homogeneous). 

tCatakH?u« recommends a maximum and minimum speed. Constants given are for the arerage 
peed. 

(Tables in catalogue based on full theoretical power of the water. Wheels are said to give from 
rs per cent to 90 per cent efficiency, depending on location. 

^Munson Bros. Co. make several types of **Little Qiant** turbines causing above wide variation 
in constants. 



It is evident that K4 is constant for all turbines with constant K 
and Kg ; also, for all turbines where q, the discharge, is equal at the 
same speed, n, and under the same head, h, K^ must be constant for 
different heads since n and q are proportional to V^- The values of 
the constant K^ as calculated from the tables contained in the 
catalogues of various American manufacturers are given in Table 
XXXI. 

164a. Relation of Speed to Power of Turbines. — From equation 
(35) may be derived 



(53) 



q = 



8.8 P 
eh 



348 Hydraulics of the Turbine, 

From equation (48) may be derived 

(54) K, i/K = 12 X ^ X i/h" ^ vT 

Combining equations (53) and (54) 

(66) K.V/K =^I2^n4/5 

12 X GO^e h" 

By transposing 



(66) 



K,Vk 12X60 /V = n i / L 



As the first member of the equation is constant for any given 
wheel, there may be written 

(57) K, = ^^ ViJ J 

and hence 

(68) K. = I.' ^. 

From equation (58) it will be noted that the value of K5 under a 
given head is in direct proportion to the square of the velocity of 
the wheel and to its power. Kg is termed the "specific speed" of the 
wheel. A high value of Kg is an indication of high speed, and a 
low value, of low speed. 

The values of the constant Kg as calculated from the tables con- 
tained in the catalogues of various manufacturers of American 
wheels are given in Table XXXII. 

Fig. 222 shows graphically the relation of power to speed under 
one foot head, as expressed by the constant Kg within the range of 
practice of American turbine builders. 

The use of the diagram may be illustrated as follows : — 

At 35 revolutions per minute various types of American wheels 
will develop from i to 5.8 horse power. For the best efficiency, 
that is for a constant value of <^, the number of revolutions ot a 

wheel will vary as Vh, and the power will vary as h*. Thus foi 
a 16 foot head these wheels will run four times as fast as for a on« 
foot head or at 140 R. P. M., and will develop 64 times the power 
that will be developed at a one foot head, or from 64 to 371 H. P^ 
between which limits the wheel must be chosen. 

Suppose a wheel is desired to develop 500 H. P. at 150 R. P. M. 
under 25 foot head. These conditions correspond to 4 H. P. at Jo 



Relation of Speed to Power of Turbine. 



349 




3 4 s e r s I 

MQflSC POWEH moeil DIK FOOT KCAD . 



Jl 



Fi£. 222.— Speed Curves of Various Standard American Wheels. 



350 



Hydraulics of the Turbine, 



TABLE XXXII, 

JShi^wing Relation Qf Speed and Pon>er o/' Various American Turbine*^ 
under Catalogue i and it ions. 



K, = n* 



b| 



MAnufactnrer. 



Name of Wheel, 



K, 



MitL Mw 



Eeaction WhMU. 

T. C Alcott &So]i^,,,,.>>.. 

Alexander, Bradley de Dunn 

ing*,... 

American Steel Dredge Wrke 
Ganideji Water Wheel Works 
Chase Turbine Mfg. Co 



OhriHtiana Machine Cb... . * , 
Craig, Rid g way A Son Co.. , , 
Craig, Ridgway d Son Co.. . . 
Dayton Globe Iron Worka Co. 



J. L, &8.B.Dii.„. 

Dubuque Turbine A Roller 

Mill Co 

Dubuque Turbine 6l Roller 

MiirCo 



Ho) yoke Machine Co** * * 
Httmpbrey Machine Co. 



Rodney Hunt Machine Co. 



E. D. Jones A Song Co, 
Janiea Leffel & Co-« . .. . 



Miuieoii Bros. A Co 

Norriab, Burnham & Co* 
Piatt iron WortiB Co. . . . 



Alcotfa Standard High Duty 
Alcoli'i ^^peciat High Duty. 

Syracuse Turbine. » 

*Little Giant. ............ 

United States Turbine 

*Chase-Jonval Turbine (reg- 

ular) ,,,,,.....,.,..,..*. 
•CbaFe-Jonval Turbine 

(epecial ) ,•-.... 

Balanced Gate Turbine. ... 
Double Perfection, i •••.,♦.. 

Standard 

* American Turbine. ....... 

fNew American (high head 

t)T>e)..- 

Improved New American 
Special New American . . . 
Improved Jonval Turbine 



Fleimiken Turbine, 



McCormick's Holyoke Tur- 
bine ....•.<,,..*.., 

Herctilea Turbi ne * « « , < . * t * . 

JIXL Turbine 

tXLCR Turbine 

McOormick*! Uolyoke Tur^ 
bine 

*Hunt McCormick Turbine. 

*New Pattern Hunt Turbine 

•i^tandard Wheel » lti8T Pat- 
tern , , 

Crocker W heel • . . • . « • . . 

f^amson ^ . 

Improved 8ameoQ 

Standard.. 

tfpboenii' '^Littfe dfant" 



Victor Regisier Gate 

Victor Standard Cylinder 

Gate \.,, 

Victor High PreBSure* . . . * 



941 
2152 

723 
2880 
3780 

1680 

S4riO 

1220 

840 

77fi 

623 

520 

6100 
2490 

1360 



2S80 

2030 

572 

1052 

2310 
2360 
1624 

1666 
2360 

H775 
5013 

948 
17:^ 

843 

li:w 
2254 

37.S3 

129,10 



1216 

m 



la 
m 

flf75 

im 

674 

m: 
isao 



^9 

m 
1^ 

MO 

31110 
2W0 

2180 
26110 

5400 
lOfiS 
1^^ 
IfiOO 
im 
2712 






m 



Relation of Speed to Power of Turbine. 351 ^^B 

TABLE XXXII.— Coniintied. ^^B 

Showing Edatvm of Speed arid Power of Various AmeHcan TurbintM t^orking ^^B 

under Cataiogtte Conditions. ^^H 


Manufacturer, 


Kanie of Wheel. 


I 


Min. 


Max. 1 


Reaction Wheels.— Con. 

^■tjol© EngioeeriDjr and Ma- 

ehinaCo.*... 

r> H- Risdon & Co. . , , -, 


Poole^LeffeL «.«••>*.* 


1170 
2350 
3520 
4690 
2640 
6165 
3307 
23B0 

12.34 
4,00 
7.84 
3.24 


1239 m 
3680 m 

5070 ^ 

7370 

3013 

6640 

42d0 

13.01 

7.62 

11.42 

11.22 


*Bi§don Standard Turbine. . 
*Ri^on Type T. C Turbine 
♦Risilon Type D. C. Turbine 
Smith McCormick , , 


8* Mofv&n Smith Co. --.***.. 


Hie Tramp Mfg. Co 

Well mail, Seaver, Morgan Co. 

Impulse Whe^s. 

DeReioer Water Wheel Co,. 

Abnef Doble Co ........«..>. 


Smith ,*B>4»«**»****. 


Standard Truint* , , 


McCormick • • . - - 


•DeRemer Water Wheel. . . . 
*TttnizentiaJ Wlieel ...,.,... 


Pelton Water AVheel Co 

Risdon Iron Works ...,.,, . 


*TanEential Wheel , . . , . 


*Tanirential Wheel 




•Wide TariatioQ in coiutaaU due u> the design belnR speclaL ior various iilxed wheeli 4 series not 
tCat&loKui: recoiuiueDclB a maxim um and inlnimuin speed. Conitatita given am for ibe averagii 

iTabJpft In c»tftJf?gne bfti#d m ftjll th'-oretic*! powtr of tli« water, WtieeU are said to glTe from 
75 j»r qi*nt to MJ per cerat ert\t:lenc,v, tit| wilding on Jocaaon, 

]^MuQ«on Broft, C^ make several typeb oF "LltUe Giant" turbines cauaEnjc aboni wide rartaUon 
in coetsi&nta. 

R, P, M. under one foot head, and would require a wheel having a 
constant Kg = 3600. 

165, Value of Turbine Constants. — The values of the constants 
discussed in this chapter have been determined froni the cata- 
logues of the manufacturers of American turbines and are the %'alues 
which may be used for determining the manufacturer's standard re- 
lations of the wheel for particular and fixed conditions where <^ is 
constant, as, for example, the development of a certain power under 
a fixed head and with a given speed. When the head varies at dif* 
ferent times, the value of ^ also varies and the value of the other co- 
efficients of the turbine, A, K, K3, K4, and K^, will also vary. In 
order to discuss such conditions the laws of the variations of these 
constants, tor any series of wheels, must be known. Tliese laws 



352 Hydraulics of the Turbine. 

can be ascertained from a complete test of any one wheel of the 
series and the laws so determined will hold for the entire series if 
the series is actually constructed on homogeneous lines. Owing to 
imperfections in the processes of manufacture, there is actually 
more or less variation between diflFerent wheels of a series. It is 
therefore desirable, when the approximate size of the wheel needed 
is known, to secure a test of a wheel of that particular size and 
hand. 

Of the constants discussed, <l> and A express the standard rela- 
tion recommended by the manufacturer between diameter and speed 
in the series of wheels he offers. See equations 

(23) n = ^^^^^^and 



(24) 



D = A1^ 



The coefficient K is the constant of discharge and shows the 
standard relation for various types of turbines between the quantity 
of water discharged and the diameter of the wheeL See equations 

(41) q = K DVF and 



(^> ^=1/^^ 



Kl/h 

Kj IS the constant of power and shows the standard relation b^ 
tween the diameter of the wheel and the power. See equation 

(45) P = K,D«h* 

K^ is the constant of discharge and shows the standard r?lation 
between speed and discharge. See equation 

(50) n = K^\/^ 

q 

Kg is the constant expressing the standard relation of power and 
speed for a particular series of wheels. See equation. 

(58) ^ = ^- 1? 

The catalogue tables of turbines from which the standard values 
of the constants in the preceding tables have been calculated arc 
presumably based on the actual tests of certain wheels of the series. 
The actual results of a test of any individual wheel of the series is 
likely to depart to an extent from the tabular val*ue. Differences 



Literature. 353 

en be found between wheels of different diameters, between 
of the same diameter but of opposite hand, and even between 
of the same size and hand which are supposed to be con- 
l on identical lines. 

5 differences in results are due to carelessness in construe- 
to unusually good construction in the effort to secure special 
where the conditions warrant special effort. Any change in 
gn of a wheel for the purpose of reducing or increasing the 
rt, and hence reducing or increasing its power, will give 
differences in these coefficients which must be taken into 

in any calculations made thereon. A careful study of these 
nts as determined from the actual tests of any wheel, to- 
vith a study of the design of the wheel itself, will form the 

a complete and systematic knowledge of water wheel de- 

LITERATURB. 

ann, Gustav. Die graphische Theorie der Turbinen and Kreisel- 

pumpen. Verhaldung des Vereiues zur Befdrderung dee Gewerb- 

feisses In Preussen. 1884, pp. 307-379; 521-580. 
;, C. Graphic Turbine Tables. Showing relation of head and dis- 
charge for various sizes of turbines. Zeitschr. d ver Deutsch. 

Ing. p. 980. 1890. 
Kig, H. Allgemeine Theorie der Turbinen. Berlin. L. Simon, 

1890. 
rds, John. Turbines Compared with Water Wheels. Eng. News. 

Vol. 1, p. 530. 1892. 
ing, A. W. Notes on Water Power Equipment Jour. Asso. Eng. 

Soc. Vol. 13, p. 197. 1894. 
ner, G. Die Hydraulik und die hydraulischen Motoren. Jena. 1895. 
er, G. R. Hydraulic Motors, Turbines and Pressure Engines. New 

York. Van Nostrand. 1895. 
B, R. G. Hydraulic Machinery. New York. Spon & Chamberlain. 

1897. 
s, Charles N. Centrifugal Pumps, Turbines and Water Motors. 

Manchester. Eng., Technical Pub. Co. 1898. 
William. Graphics of Water Wheels. Stevens Indicator. Vol. 16, 

p. 30. 1899. 
T. Ernst A. Grundrlss der Turbinen Theorie. Lelpsig, S. Hirzel. 

1899. 
r, Gustav. Vorlesungen iiber Theorie der Turbinen mit vorbereiten- 

den untersuchungen aus der technischen hydrauhk. Lelpsig. 

Arthur Felix. 1899. . 
u, A. Traits des turo-machines. Paris. Ch. Dunod. 1900. 



354 



Hydraulics of the Turbine, 



14. Henrotte* X Turblnes-liydrauUques, pompea et TentUateurs, centrlfogsa. 

prlnceps tlieoriaaeai disposltlona pratiques et calcul des dlrnen- 
Eton 3. Liege, I m primer I e Ll^geoUe. 1900. 
16. Marks, G. Croiden. Hydraulic Power and Engineering. New YorL Va 
Nostrand. 1900. 

16, Wood, DeVolaon. Turblnea, Theoretical and PraeticaL New York, Wilef 

& Sons. 1901. 

17. MuIIer, Wllhelm. Die Fraacls-Turblnen. Hanover, Janecke. 1901 

15. Kessler, Jos. Berecbaung and Konstruktion der Turblneu. Lelpslg. I 

M. Gebhardt. 1902. 

19. Camerer, R* Diagrams of Tbeory of Turbines. Graphic Rpprts^nra- 

tlon of Equation with Proof and Application^ Dlngler's M? 
tech. Jour. p. 693> 1902. 

20. Tburao, Jo ha Wolf. Modern Turblaa Practice aad the Development ol 

Water Power. Eng. News. Dec. 4, 1902. 

21. Rea, Alex. Turbines and the Effective Utilisation of Water-P^Jwef, 

Mech. Engr. March 22, 1902. 

22. Osterlin, Hermann. Unteraucbungen flljer den Energleverlust des Wis- 

sera in Turblaenkanalen, Berlin. Julius Springer. 1903. 

23. ThurBO, Jobn Wolf. Effect of Draft Tube. Eng, N«wa, Vol. 1, P^ 21 

1903. 

24. de Qraffiguy, HenrL Les Turbo*motenrs et lea Machines Rotative fu\A 

E. Bernard. 1904. 

25. Dlekl. Ignaz, Die Berechnung der achaialen Actionsturbinen aaf «icli' 

nerlschem Wege- Vienna. Splelhagen 4t Schurlch. 1904. 
26* Danckwerta. Die Grundlagen der TurbJnenberechujig fur Pratlker tndl 
Studierende dea Bauingenieurf aches. Wiesbaden. C- W» ^l^§ 
del. 1904. 

27. Thurso, John Wolf. Modem Turbine Practice. New York* Van Kfl*| 

trand, 1905. 

28. Church, Irving P. Hydraulic Motora. New York. Wiley & Sons. 1^3- 

29. BasshnuB, N. Klasslftkation von Turblnen. Zeltachritt der Verenl" 

Deutsdi^er Ingenle for 1905, p, 922. 

30* Grafp Otto. Theorle, Berechnung und Konitruktion der Turbinen tsni 

dereu Eegulatoren; ein Lehrbuch fur schule und pfSJi*' 

Munich. August Lachner. 1904 and 1906. 

31. Wagenbach. Wllhelm. Neuere Turbinenanlagen. Berlin. 1905. 

32. Gelpke, Viktor. Turbines und Turbinenanlagen. Berlin. JuUW 

Springer. 1906. 

33. Pfarr, A. Die Turbinen fiir Wasserkraftbetrleb. Berlin. Julio* 

Springer. 1907. 

34. Tangential Water Wheel Buckets. The Engr. May 1, 1904, 

36. Klngsford. R. T. A Complete Theory of Impulse Water Wheels ta^ J^ 
Application to Their Design. Eng. News. July 21. 189S. 



J 



CHAPTER XV. 

TURBINE TESTING. 

166. The Importance of Testing Machinery.— A correct theory 
based on mathematical analysis forms a valuable foundation for 
machine design. In the construction of any machine, however, 
theoretical lines can seldom be followed in all details, and, even if 
this were possible, the truth of the theory must be demonstrated 
by actual trial for there are usually many factors involved which 
cannot be theoretically considered and yet affect practical results. 
In any machine much depends upon the character of the workman- 
ship, on the class gf material used, and on all the details of manu- 
facture, installation and operation as well as on design. All of 
these matters can hardly be included in a theoretical consideration 
of the subject, and it therefore becomes necessary to determine 
the actual results attained by a trial of the machinery under work- 
ing conditions. 

General observations or even a detailed examination of any 
machine and its operation can rarely be made sufficiently com- 
plete to g^ve any accurate knowledge of the quantity or quality of 
the results which it can and does accomplish. It is only when the 
actual effect of slight changes in design can be accurately deter- 
mined by careful experiment that a machine can be impro^ ed and 
practical or approximate perfection attained. 

The ease with which such determination can be made is usually 
a criterion of the rapidity with which the improvements in the de- 
sign and construction of a particular machine take place. Where 
such determinations are readily made, rapid advancement results, 
but where they are costly and require a considerable expenditure 
of time or money, the resulting delays and expenses usually so 
limit such determinations that good results are attained but slowly. 
The invention of the steam engine indicator and the Pu-^ny brake 
placed in the hands of the engineer instruments by means of which 
he could readily determine the action of steam within the engine 
cylinder and the actual power developed therefrom. The knowl- 
edge thus gained has been one of the most potent factors in the 
rapid advancement of steam engineering. 



356 



Turbine Testing, 



H ine 



The physical results of radical modifications or changes in de- 
sign are sometimes quite different from those anticipated by the 
designer. Impro\^ement in any machine means a departure bom 
the tried field of experience and the adoption of new and untried 
devices or arrangements. Frequently a line of reasoning, while 
apparently rational^ is found to be in error on account of unfore* 
seen conditions or contingencies and the resulta anticipated are 
not borne out in the actual practical results. Unless, therefore, 
such results are carefully and accurately determined by exact 
methods the actual value of changes in design may never be knows 
or appreciated and designs may be adopted which, while apparently 
giving a more desirable form of construction, actually accomplish 
less than the form from which the design has departed, 

157, The Testing of Water Wheels.— The value of the testing ol 
water wheels was recognized by Smeaton who- tested various 
models of water wheels about the middle of the Eighteenth Century, 
Methods of turbine testing were also devised with the first develop- 
ment of the turbine, which have been potent factors in the improve- 
ment of the turbine. While the methods of testing have been 
greatly improved since that time, they have not as yet reached a 
state that can be considered reasonably satisfactory, and turbine 
testing has not become so general as to assure the high grade of 
design and workmanship in their manufacture as in other machin- 
ery where testing is more easily and regularly practiced* 

The principal causes of the backward condition of turbine test- . 
ing lie in the difficulties and expense of making an accurate test ] 
in place, and the expense and unsatisfactory results of testing tur- 
bines in a testing flume where the head and capacity are so limited 
as to confine satisfactory tests to heads of 17 feet or less and toj 
wheels of a capacity of about 250 cubic feet per second, or less M 
the full head of 17 feet is to be maintained. There is an urgent 
demand for accurate and economical methods for the measurement 
of the water used and of the power developed by water wheels in ! 
place, that can be readily and quickly applied without the almost | 
prohibitive expense of the construction of expensive weirs and 
other apparatus now used for such purposes. Apparently slight 
variations in turbine construction produce radical changes in prac- 
tical re?>ults. The high results achieved under test by a well- 
designed and well-constructed wheel is no assurance that wheels 
of the same make and of the same design, even though they be t( 
the same size and even from the same pattern, will give sim'uar 




Smeaton's Experiments. 



357 



This IS especially true when the contingencies of compe- 
id the knowledge that a test of the wheel is impossible, or 
highly improbable, offer a premium on careless construe- 
cheap work. 

*f examination of the work already done in this line, and 
lethods now in vog^e, may afford suggestions for future 
ments and development in this important work. 
meaton's Experiments. — John Smeaton, the most experi- 
id eminent engineer of his time, made a series of experi- 
n the power and effect of water used by means of various 
water wheels for mill purposes. Accounts of these experi- 
ere published in the Transactions of The Royal Society of 

England in 1759. Until that 
time the relative values of the 
different types of water 
wheels of that day were very 
poorly understood and ap- 
preciated. 

Smeaton's apparatus for 
measurement of the power 
of" overshot and undershot 
wheels is shown by Figs. 223 
and 224 taken from **The 
Encyclopedia of Civil En- 
gineering" by Edward 
Cressy. Water was pumped 
by means of the hand pumps 
from the tail basin, X, to the 
supply cistern, V, from which 
it was admitted to the wheel 
through an adjustable gate. 
The power developed was 
measured by the time re- 
quired to raise a known 
weight through a known 
height by means of a cord 
through a system of pulleys and attached to a small wind- 
I or collar upon the wheel shaft. This drum revolved only 
r slight longitudinal movement, it was made to engage a 
le shaft. 
se experiments Smeaton found a maximum efficiency of 




Bmeaton's Apparatus for Testing 
Water Wheels. 



35S 



Turbine Testing. 



32 per cenL, and a minimum efficiency of 28 per cent, for undershot 
wheels. He also observed that the most efficient relations between 
the peripheral velocity of the wheel and velocity of tlie water were 
attained when the former was from 50 per cent, to 60 per cent of 
the latter, and that the force that could be exerted by a wheel to 

f 




Fig 224.— Section of Smeatoii'B Apparalna for Testing Water Wbeeli 

advantage was from 50 per cent, to 70 per cent, of ilie force re- 
quired to maintain it in stationary equilibrium. 

For overshot wheels Smeaton found that the efficiency varied 
between 52 and 76 per cent* From his experiments he concluded 
that the overshot wheel should be as large as possible, allowinf. 
however, a sufficient fall to admit the water onto the wheel witli^ 
velocity slightly greater than that of the circumference of the 
wheel itself, and that the best velocity of the circumference of th< 
wheel was about three and one-half feet per second. This spc< 
he found applied both to the largest as well as to the smallest 
water wheel. 

From these experiments Smeaton concluded that the power of 
water applied directly through the exertion of its weight by gia^ 
ity, as with the overshot wheel, was more effective than when its 
power was applied through its acquired momentum* as in tht 



i 



The Early Testing of Turbine Water Wheels. 359 

-undershot wheel, although his line of reasoning indicated other- 
-wise. The later development of impulse wheels shows that his 
reasoning was correct, and that the low efficiency of the impulse 
'wheel was due to the method of applying the momentum of the 
iwater rather than to any inherent defect in the impulse principle. 
The experiments or tests of Smeaton, while crude and imperfect 
and performed upon wheels which were merely models, afforded 
a comparative measurement of the efficiency of the undershot, over- 
shot and breast wheels then in use and had a marked effect on the 
further selection of such wheels. 

169. The Early Testing of Turbine Water Wheels.— The testing 
of turbine wheels began many years ago in France before the turb- 
ine became well known in the United States.* 

Foumeyron began the study of the early forms of turbines as 
early as 1823, and, in 1827, he introduced his well-known wheel 
and also brought into notice a method of systematic testing of the 
same by means of the Prony brake. 

"La Society d' Encouragement pour V Industrie Nationale" is 
credited by Thurston with the introduction of a general system for 
the comparison of wheels and correct methods of determining the 
efficiency.** Other engineers immediately accepted this method of 
comparison of wheels. Morin, in 1838, reported the results of a 
trial of a Fourneyron wheel as giving an efficiency of 69 per cent, 
with only slight changes in values for a wide range of speed. With 
another wheel he obtained 75 per cent, efficiency.! 

Combes tested his reaction wheel and found that an efficiency 
<rf about 50 per cent could be obtained.! 

The first systematic test of turbines in the United States was 
made by Mr. Elwood Morris of Philadelphia in 1843 ^rid reported 
in the Journal of The Franklin Institute for December of that year. 
The maximum efficiency reported was 75 per cent. This result 
was reached when the value of <l> for the interior circumference of 
the Foumeyron turbine was .45. In 1844 Mr. James B. Francis 
determined the power and efficiency of a high breast water wheel 



• See "The Systematic Testing of Water Wheels In the United States," by 
H. H. Thurston, Trans. Am. Soc. Mech. Eng. vol. 8. 

♦♦ See "Memolre sur les Turbines Hydrauliques," by H. Foumeyron, Brus- 
sels, 1840. 

t See "Experiences sur les Power Hydrauliques/' Paris, 1838. 

t See 'Mechanics of Engineering," Weisbach. Translated by A. J. DuBois. 
Hydraulics and Hydraulic Motors, vol. II, part I. p. 470. 



36o 



Turbine Testing, 



I 

I 



in the City of Lowell, usin^ a Prony brake fitted with a dash-pot 
to prevent irregular operatian. 

In 1845 Mn Uriah A, Boy den made a trial of a turbine designed 
by himself, using the Prony brake, and obtained an efficiency 0178 
per cent, as the maximum. In 1846 a similar test of one of the 
Boyden turbines was made at the Appleton Mills in Lowell, mi 
an efficiency of 88 per cent, was reported. He continued the work 
of the testing of water wheels for several years and tested manv 
wheels of various types.* Mr. Francis introduced the system of 
testing wheels which were to be used by purchasers of water from 
the water power company which he represented. The chief pur- 
pose of the tests was that the wheels might be used as meters in 
determining the amount of water used by the various purchasers, 

In i860 the City of Philadelphia undertook a comparative tniJ 
of various turbines in order to determine their relative merits tor 
used in the Fair mount Pumping Plant, The results o^f these tests 
given in Table XXXIII are somewhat questionable but have i 
comparative value. 

TABLE XXXIIL 
Water Wheel Ttsta at PhUaijkJphia in ISBQ, 



Name of Wheel. 


Kind of 

Wheel. 


Per 

cent 

of 

Effect. 


3 pet- 
cent 
added 

for 
frier n 


Whete built. 


Steveneon'e eecond wheel - 

Geyelin'fl fiecontl wht^el ,,,..,... 


Jonval . . 

Jonval .. 
Bpii^K,. 
Jonval . . 

Spiral... 
Spiral , , . 
Spiral... 
Jonval , . 

Scroll . . . 
SCToli , . . 
Jo rival . , 

Spiral . . . 
Scroll . . . 
Scroll . . . 
Spiral . , . 
Scroll... 
Spiral.., 
Scroll . . . 
Jonval . . 


,8777 
.8210 

*8197 
.7672 

.7691 
.7669 
,7457 
.7335 
,7169 
,7123 
.6799 
.0726 
.6412 

.62€5 
.6132 
.5415 
.5359 
.4734 


.9077 
.8510 
.8497 
.7972 

.7891 
.7869 
,7767 
.7635 
.74^9 
.7423 
.7099 
.7026 
.6712 
.6624 
,6605 
.6432 
,5715 
.5659 
.5034 


PatcTson, X. J 

Philadelphia. Fit. 
Berovirie, Pa. 

TroT N Y 


Andre wg ^ K&lbaeh'e third wheel 
( 'oHift'i, EifCfiiid wlieel ........... 


Andrews 4b Kalbach'e eecond 
wheel ,.,.,,.,..«,., ......... 


Bemville Pa. 


Smithes, Parker^B fourth trial , . . . 

Smith's, Parker's third trial 

Kteven's l9,rst wheel. , » * * * 


Readinir, P*. 
Heading, Pa. 
Patereon N J, 


Blake - 


East Peppered M»»^ 
Weit Lebanon. N H. 


Tyler .......---. * 


Geyelin*a first wheel ,.*........ 


Philadetphu, F^, 
H«adiii«, Ph. 
Guilford. N. Y, 


Smiih*^, Parker's second wheel. . 
Merchant's Goodwin 


Maeon's SEtiUb .....»* 


Buffalo, N T. 


Andrew^s first wheel •«.. 


Bemville, P*. 


Rich ♦ ..,,,.*,..* ^ »»........ . 


Salmon River K. T 


I*i til^T>tt#e ..iiiiT.»»«Tf'- 


Anstiiii Texa^ 


Monroe ....#« >■■ .. 


WoiresK^f, Man, 


Collin's Erst, wheel *......* 


Trov, N Y 







The Testing of Turbines by James Emerson. 361 

170. The Testing of Turbines by James Emerson, — One of the 
en who did much valuable work of this character was Mr. James 
merson who designed a new form of dynamometer of the trans- 
itting kind. At the request of Mr. A. M. Swain, Mr. Emerson 
^signed a Prony brake, embodying this dynamometer for the pur- 
)se of testing a Swain turbine in a flume built from designs by 
rands. The results obtained by Mr. Emerson from this test 
ere so satisfactory that The Swain Turbine Company decided to 
)en the flume for the purpose of a competitive test of all turbines 
hich might be oflFered for this purpose. Announcement of this 
St was dated June i6th, 1869. The pit was fourteen feet wide, 
lirty feet long, and three feet deep, measured from the crest of the 
eir. The best results of this competitive test, the accuracy of 
hich has since been questioned by Mr. Emerson, were attained 
ith the Swain and LeflFel wheels. The former ranged from 66.8 
p to 78.9 per cent efficiency, and the latter from 61.9 to 79.9 per 
ent efficiency. This competitive test was the beginning of a series 
f such tests as well as of a general system of the public testing of 
irbines. The testing flume was opened to all builders and users 
f turbine wheels and such tests have been continued in the United 
tates up to the present time. 

The report of the results of this test attracted the attention of 
fr. Stewart Chase, then agent of The Holyoke Water Power Com- 
any, who, recognizing its very great importance, secured the 
doption of a systematic testing of water wheels at Holyoke for 
le benefit of the Company and wrote to Mr. Emerson as follows : 
'The testing of turbines is the only way to perfection, and that 
i a matter of great importance. Move your work to Holyoke and 
se all the water that is necessary for the purpose, and welcome, 
ee of charge." 

Mr. Emerson, who had been conducting the testing of water 
heels as a matter of private business at Lowell, at which place 
t was obliged to pay for the water used, at once accepted the 
beral oflFer thus tendered him and removed to Holyoke where he 
mtinued the testing of water wheels until it was taken in hand 
r The Holyoke Water Power Company. 

The reports of Mr. Emerson's work were published and undoubt- 
ly were the means of bringing a number of wheels up to a state 
high efficiency. The reports were found to be full of valuable 
22 



362 



Turbine Testing. 



data, and, although not systematically arranged, formed an exten- 
sive and valuable collection of figures. "*" 

In 1879, The Holyoke Water Power Company, for the purpose of 
determining the standing of wheels offered for use at that place, 




I GATE 



Fig. 225. 



arranged for a coimparative or competitive turbine test at the flume 
constructed by Mr. Emerson at Holyoke. The wheels were fd 
under the direction of Mr. Emerson and a part of the tests were 



♦ See James Emerson's "Hydro-Dynamics." 



The Testing of Turbines by James Emerson. 



363 



ade or witnessed by Mr. Samuel Weber and Mr. T. G. Ellis. 
heir report was accompanied by a graphical diagram (Fig. 225 
id Table XXXIV) on which they commented as follows : 
"By examining' the diagram and table, the peculiarities of the 
veral wheels will be readily seen. It will be observed that the 
>uston turbine, which has the highest percentage of effect at full 
te, is really the least efficient at from half to three-quarters, and 
)m half to full gate, of all those shown on the diagram, and is 
ly superior to the Nonesuch at from three-quarters to full gate, 
d that by a very trifling amount; so that the wheel which ap- 
rently has the highest percentage is really the least desirable for 
tnal use. The Thompson turbine, which has the lowest percentage 
those shown at full gate, rises to the sixth place at from one-half 
full gate, and to the fourth place at from one-half to three-quart- 
5 gate. The Tyler turbine, which has the second highest per- 
ntage at full gate, falls to the sixth place at from one-half to 
ree-quarters gate. The Hercules turbine, which stands third 
ly at full gate, takes the first rank at from half to full gate, or 
ly of its subdivisions. The New American turbine, which stands 
ly fifth in the percentage at full gate, is second only to the Her- 
les at from one-half to full gate or either of its subdivisions, and, 
deed, differs from the Hercules very slightly in its useful effect 
rough the whole range shown. 

"Taking the average useful effect of the wheels shown from one- 
If to full gate as a measure of their efficiency, their relative value 
in the order shown in the table." 



TABLE XXXIV. 
Showing Average Percentage at Part Gate, 



Name. 



Hto9i 
Per cent. 



H to Full 
Per cent. 



K to Full 
Per cent. 



rcules 

r American 

sees 

Br 

mpson .... 

eiucb 

iston 



.737 
.732 
.708 
.605 
.680 
.696 
.619 
.397 



.805 
.795 
.786 
.766 
.744 
.721 
.712 
.717 



.771 
.763 
.747 
.716 
.712 
.709 
.666 
.557 



364 



Turbine Testing, 



The report of Mr. Emerson covered a much larger number or 
wheels. The diagram accompanying Mr. Emerson's report* is re* 
produced in Fig. 226. 




I GATE 



FDILJ 
eiETCj 



i^ 



Fig. 220. 

171. The Holyokc Testing Flume, — The later work of systen 
testing of American turbines has been carried on principally at ! 
Holyoke flume. 

t 'The object aimed at by the Water-power Companies of Lowc 
and Holyoke, in the establishment of testing flumes for turbin 

* Emerson's "Hydro^Dynamlcs," page 300. 

t*The Systematic Testing of Water Wheels/* by H. H. Thurston. 



The Uolyoke Testing Flume. 365 

the determination of the power and efficiency, the best speed, 
d the quantity of water flowing at from whole, to, say, half gate, 
exactly that the wheel may be used as a meter in the measure- 
int of the water used by it. The quantity of water passing 
x>ugh the wheel, at any given gate-opening, will always be prac- 
ally the same at the same head, and the wheel having been 
ted in the pit of the testing flume, and its best speeds and highest 
ciency determined, and a record having been made of the quan- 
j of water discharged by it at these best speeds and at all gates, 
\ turbine is set in its place at the mill, speeded correctly for the 
id there afforded, and a gauge affixed to its gate to indicate the 
:ent of gate opening. The volume of water passing the wheel 
various openings of gate having been determined at the testing 
me, and tabulated, the engineer of the Water-power Co. has 
ly to take a look at the gauge on the gate, at any time, or at regu- 
times, and to compare its reading with the table of discharges, 
ascertain what amount of water the wheel is taking and to de- 
mine what is due the company for the operation of that wheel, 
that time. The wheel is thus made the best possible meter for 
t purposes of the vender of water." 

The present Holyoke Testing Flume was completed in 1883. 
le plan of this flume is shown in Figs. 227 and 228. 
The testing flume consists of an iron penstock, A, about nine feet 
diameter, through which the water flows from the head race 
:o a chamber, B, from which it is admitted through two head 
tes, G,G, into the chamber, C, and from thence through trash 
cks into the wheel pit, D. Passing through the wheel to be 
sted, it flows into the tail-race, E, where it is measured as it 
»ws over a weir, at O. The object of the chamber, B, is to afford 
portunity for the use of the two head gates, G,G, to control the 
mission of water, and consequently the head acting on the wheel, 
lere is also a head gate at the point where the penstock. A, takes 
water from the first level canal. A small penstock, F, about 3 
!t in diameter, takes water from the chamber, B, independently 
the gates and leads to a turbine wheel, H, set in an iron casing, 
the chamber, C, in order that this wheel can run when C and the 
leel pit, D, are empty. The wheel, H, discharges through the 
or at the bottom of C, and through the arch, I, and the supple- 
ntary tail-race, K, into the second level canal. This wheel is 
id to operate the repair shops ; also to operate the gates, G. The 
imber, C, is bounded on one side by a tier of stop-planks, L, and. 



366 



Turbine Testing. 



k. 




The Holyoke Testing Flume. 



367 



on another side, by a tier of stop-planks, M, The object of the 
stop-planks, L, is to afford a w^ste-way out of the chamber, G 
This is of especial use in regulating the height of the water when 
testing under low heads. The water thus passed over the planks* 
L, falls directly into the taiUrace, K. and passes into the second 
level. The stop-planks, M, are used when scroll or cased wheels 




1 — BTHTiiwrinnrifTi 



Fig. 228. —lasting Flume of Holyoke Water Power Co, Arranged for Teeting 
Horijtmitfll Turbinefi. 

are tested. In such cases D is empty of water and the wheel case 
in question is attached by a short pipe or penstock from an open- 
ing cut in tile planks, M. Fhimc wheels are set in the center of the 
floor of D, and D is filled with water. They discharge through the 
floor of D and out of the three culverts, N,N,N, into the tail-race^ 
E, Horizontal wheels are set in tlie pit, D, with their shafting 
projecting through a stuffing-box in the side of the pit (See Fig. 
228). At the down-stream end of the tail-race is the measuring 
wetr, O (Fig. 227), The crest of the weir is formed of a strip of 
planed iron plate twenty feet in length. The depth of water on the 
weir is measured in a cylinder, P, set in a recess, Q, fashioned in 
the sides of the tail-race. These recesses are water-tight, and the 
observer is thus enabled to stand with the water-level at convenient 




368 Turbine Testing* I 

height for accurate observation. The cylinder, P, is connected wit^ 
a pipe that crosses the tail-race or weir box about ten feet back of 
the weir crest. The pipe is placed about one foot above the Soar 
and is perforated in the bottom with i inch holes. A platfonn, K 
surrounds the tail-race, and is suspended from the iron beams thai 
carry the roof. Above the tail-race is the street, over which xht 
wheels to be tested arrive on wagons from which they are lifted 
by a traveling crane that runs on a frame-work over the street, and 
by means of which the wheels are carried into the building and art 
lowered inEo the wheel pit, D. Spiral stairs lead into a passageway 
that leads in turn to the platform, R. In the well-hole of these 
stairs are set up the glass tubes which measure the head of water 
upon the wheeh These gaug^e tubes are connected with the pit, D. 
and the chamber, C, by means of pipes, one of which enters the 
wheel pit through a cast iron pipe^ T, built into the masonry dam 
which forms the down stream end of the wheel pit, D. The other 
pipe passes back under the wheel pit, D> and crosses the tail-race 
at the extreme back line and close under the pit floor. This pipe 
is perforated throughout its length across the race in a manner 
similar to the pipe used for determining the head on the weir. To 
enable the observers at the brake wheel, head gauge and measuring 
weir to take simultaneous observations, an electric clock rings 
three bells, simultaneously, at inter\^als of one minute. 

The usual method of testing a wheel is as follows: After tlie 
wheel 15 set in place (See Figs. 227 and 228) a brake pulley and 
Prony brake are attached to the shaft, the gates arc set at a fi-xcd 
opening and water is admitted. The runaway speed of the wheel 
is first determined with the brake band loose, after which a wci^hi 
is applied and the brake tightened until the friction load balances 
the weight. As soon as this balance is attained, which requires 
only a few seconds, the revolution counter is read and the head? 
in the head-race, tail-race and on the weir are observed. Obsen^^i' 
tions are repeated simultaneously each minute at the stroke of the 
bell and for a period of from three to five minutes. The weight 
is then changed and the observations repeated for a different load 
and speed. After observations are made over the range of speed? 
desired, the gate opening is changed, and a similar series of obser- 
vations are made for the new gate opening. This is repeated (of 
each desired gate opening, usually from full gate to about one-half 
gate. 

The results are calculated and reported in the form shown in 
Table LX. It is usually stated in the report whether the test is 




^ 



The Value of Tests. 369 

de with a plain or conical draft tube, whether plain or ball bear- 
s are used, and also the pull necessary, at a given leverage, to 
rt the turbines in the empty pit. No attempt is made in these 
orts to describe the bearings or finish of the wheels in detail. 
The maximum head available is about 17 feet under small dis- 
Tges and this decreases to about 9 feet under a discharge of 300 
)ic feet per second. The capacity of the tail-race and weir is 
dly sufficient for the accurate measurement of the latter quan- 

r 

7a. The Value of Tests. — ^There can be no question as to the 
•y great value of carefully-made tests of any machine. It must 
borne in mind, however, that any test so made represents results 
ler the exact conditions of the test, and, in order to duplicate the 
ults, the conditions under which the test was made must be 
plicated. Any changes in the design or finish of the wheels, any 
orations in the method of setting, or in the gates, draft tube or 
ler appurtenances connected with the same are bound to affect 
: power and efficiency to a greater or less extent. 
it is unfortunate for the world's progress that the records and 
iditions of failures are seldom made known. The record of a 
lure, while of great value from an educational standpoint, may 
isiderably injure the reputation of an engineer or manufacturer, 
i consequently results of tests and experiments, unless fully 
isfactory, are seldom published or known except by those closely 
crested. For this reason, the published tests of water wheels 
lally represent the most successful work of the maker and the 
;t practical results he has been able to secure. Tests, unless 
iy representative, do not assure that similar turbines of the 
ne make, or even similar turbines of the same make, size and 
tern, will give the same efficient results unless all details of their 
ign, construction, and installation are duplicated. There is no 
ibt that in many cases the published tests of water wheels are 
final consummation of a long series of experiments, made in 
!cr to secure high results, and do not give assurance that such 
ults can be easily duplicated. The manufacturers have acknow- 
g^cd this by calculating their standard tables on a basis of power 
I efficiency below that of the best tests they are able to obtain, 
I it is only a matter of reasonable precaution for the engineer, 
3 is utilizing the results of any such tests for the purposes of 
design, to discount the test values to such an extent as will 
ire him that his estimates will be fulfilled. 



372 



Turbine Testing, 



i 



The total losses given above correspond well with current prac- 
tice. Under the best conditions efficiencies greater than 83 per 
cent, are often obtain ed^ and, under unfavorable condition's with 
poor design and poor construction, efficiencies much less than the 
minimum of 72 per cent, are common. While these losses can never 
be entirely obviated they should be reduced to the practical mini- 
mum that good design and good workmanship will permit, 

175. Measurement of Discharge* — The discharge, q, of the wheel 
is commonly measured in cubic feet per second and should repre 
sent only the actual discliarge through the wheel itself. This dis- 
charge is usually measured, after it has passed the wheel, by the 
flow over a standard weir. Any leakage around the wheel into ibe 
weir box or from the weir box around the weir must be determined 
and deducted from or added to the amount passing the weir. The 
actual weir discharge must be known either by a direct calibration 
of the weir or by the construction of the weir on lines for which 
the discharge coefficients are well established. Errors in weir 
measurements often reach values of nearly 5 per cent due to the 
erroneous use of coefficients obtained from other weirs not strictly 
comparative. 

The head on the weir must be accurately determined by nican^ 
of a hook gauge which should usually read to *ooi of a foot. An 
error of .01 foot in reading the head on the weir represents about 1 
per cent,, and an error of ,001 about .1 per cent,, in the computed 
discharge with a 1.5 foot head on the weir and a much greater error 
at a lower head. 

The construction of weirs in the tail-race of power plants, es- 
pecially where large quantities of water are used under low heads, 
involves an expense which is often prohibitive. In addition to thi^ 
the construction of such weirs in plants working under low heads 
wculd often seriously reduce the head and alter the working 
conditions. 

Other methods of accurately determining the flow should be 
developed. There are two methods which seem to give proinise] 
of good results: 

First : By the careful determination of the velocities of flow io I 
the cross-section of the head or tail-race at points far enough fromj 
the wheel to guarantee steady flow. This may be done by meatisj 
of a carefully calibrated current meter, a pitot tube, or by floats ( 
To secure good results these instruments must be in the hands otl 




Measurement of Head. 



37J 



familmr with their use and with the sources of error to which 
xh is liable if carelessly used. (See Chapter XL) This method in- 
>lves no loss in head. 

Second: By the construction in tlie head or tail race of sub- 
ergcd orifices of known dimensions and of a character for which 
c coefficient ol discharge has been determined. Some work in 
is line has been done at the University of Wisconsin (See pages 
; to 45) which will soon be made accessible in detail in a bulletin 
>w in press. This method will involve only small losses of head 
id by a sufficient range of experiments can perhaps be made 
sarly as accurate as weir measurements. 




Fig. 229.— Doble Tangential Wheel Arranged for Brake Test, 



176* Measurement of Head* — ^The power of water applied to the 
^lieel depends on both quantity and head. The head is more easily 
iieasured than the quantity* but, nevertheless, requires consider- 
ble care for its accurate determination. 

The head on the wheel must be measured immediatly at the 
heel both for the head-water and tail-water. If measured some 
istance away it is apt to include friction losses, which should not 
! charged against the wheel in raceways, penstocks and gates, 
he measurement of head should usually be to about .01 feet, al- 
ough this depends on the magnitude of the heads involved. 
i77< Measurement of Speed of Rotation. — The speed of the 
iccl is usually recorded in revolutions per minute and may be 




J 



374 



Turbine Testing, 




Fig, 230,— Section and Pliiii of App«mtiis for Testing SwAin Ttirbini (bj 
James B. FmnciH). 





^^^^^B^^flr Measurement of Powen 375 

determined by a revolution-counter which records the number of 
revolutions made in a given interval of time; or by a "tachometer*' 
which, by means of certain mechanism, indicates at once on a dial 
the revolutions per minute* The latter method is more convenient 
if the instrument is correct, but frequent calibration and adjustment 
are necessary and a correction must usually be applied to values 
thus observ'ed. 

The revolution-counter is more accurate, and» while not so con- 
venient, is to be preferred. 

178* Measurement of Power, — ^Tbe power of the wheel may be 
determined by placing a special brake pulley on the turbine shaft 
^nd applying a resistance by means of a Prony brake or some other 
(arm of dynamometer. This resistance is then measured by some 
form of scales (See Figs. 229 aijd 230). The power thus consumed 
by the friction of the brake can be calculated by equation (i) 
*,^ „ 2?f 1 n w , 

P = Hor&e power 
^^^^^ 1 = length of lever or brake arm from center of revolutioiii in ft 

^^^^H n s revoluiloQ per minute, 

^^^^V jr = ratio of the circumference to the diameter of a circle = 3.1416* 

^H^ w = weight on the Bcale in pounds. 

This is the method applied in all laboratory work (see Fig. 229) and 
is that used at the Holyoke Testing Flume. If properly applied, 
it is probably subject to minimum error- When wheels are tested 
in place, it is sometimes more convenient, and often essential^ to 
determine the power output from the current generated by elec- 
trical units, which, when measured by aid of the known efficiency 
of the generator, will give the actual power of the wheeL If these 
units be direct-connected so that little or no transmission loss is 
involved, and if the generator is new and its efficiencies have been 
accurately determined, the errors involved by this method are 
comparatively smalK The transmission of the power before mea- 
surement through gearing, through long shafts and bearings or by 
other means, involves losses, the uncertainties of which must be 
avoided if accuracy is essential. 

179, Efficiency* — The efficiency of a machine is the ratio of 
energy delivered by the machine to that which was supplied to it 
and it may have various significations. 

In an impulse wheel (See Section 152) the theoretical energy of 
the water in the forebay in foot pounds per second is; 
(2) E ^ qwh 




3/6 



Turbine Testing* 



The energy just inside the outlet of the pipe is 

(S) El =qwth' ^^h') 

The energ^^ of the jet is 

(4) B. = -S5^ 

and the theoretical power delivered to the bucket is 



(fi) 



E. = 



qw (1 — <p) V {1 — cos a) tp v 



If e represents the actual ft lbs* of work delivered by the wheel 
per sec. then I 

(6) -p- = the efficiency of the entire higtallation including pipe, jet, 1 

wheels et^. ' 

(7) -g— ^ efficiency of the water wheel, including nozzle and bucket 

(8) -^^ = efficiency of the nuiner, and 



(9) 



K, 



hydra alic efficiency of the bucket 



In the testing of water wheel s» the efficiency (7), -^^ is the ratW 

j^i J 

ordinarily to be determined since it involves the losses in tlie no 

1 L* MUM J 




T 
li 







--f— n y H I ra— — 



1 r 



I i 

\ I 
1 I 
« I 

> I 

I I 



IM 



4 I 



!> 









zle, jet and buckets as well as from residual energy in the 
discharged by the buckets, all of which are properly chargeable • 

the operation of the wheel. 



Measurement ot Power. 



377 




r.ar«iir PwtSldeSlavAUon 



Fig. 232. 



SadElavatloD 

vr.aiMir 




Fig. 233. 

efficiency represented by (9) involves only the effects of 
of energy by the water in passing over the buckets and 

joretical value is 100 per cent, for all values of ^. It dim- 
the effect of uneconomical speed of rotation of the wheel 
leaves residual lost energy in the water discharged by the 

s and not properly chargeable to bucket imperfections. It 
23 



^H 37S Turbme Testing, ■ 

^m would be determmed only in a detailed study or test made for ik 
^m first purpose above mentioned* 

H 180 Illustration of Methods and Apparatus for Testing Wat« 
^1 Wheels: — Fig. 230 shows the apparatus used for testing turl^ina 

^^^ on a vertical shaft, by Mr. J, B, Francis to test a Swain wheel at tht 


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dfli 




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4 

Boo 
peril 

Tl 
testi 

T] 

In 
cour 
shaf 
moti 
1 dasli 
for 5 

Fi 
tails 


9 10 ID 70 la KB 

fsm GEirr batc oPEMmt 
Fig. 234. 

tt Mills, Lowell, Massachusetts (Sec ''Lowell Hydraulic 

ments/*) 

^e section represents a vertical turbine in the testing plant 

ng apparatus in place. 

iie plan of the plant shows the arrangement of the Prony bf 

these drawings P is the friction pulley; b is the brake; c 
iter balances to remove the load of the brake from the w 
t; L is the bent lever or steel beam for transferring horizc 
on to a vertical lift; S is the scale pan for the weight; d is 
i-pot; w is the weir for measuring the water, and r is the i 
stilling the water after leaving the wheel 
gs* 231, 232, 233, show the brake wheel and Prony brake 

used by Mr. William O. Weber for determining the effici* 


Ex- 

•akt 
are 
bed 

Wltll 

the 
rack 

d^ 



Tests of Wheels in Place. 



379 



of various turbine water wheels as described by him in a paper on 
"The Efficiency Tests of Turbine Water Wheels," (See vol. 27, No. 
4, American Society of Mechanical Engineers). (See also Section 
171, Experiments at the Holyoke Testing Flume.) 

181. Tests of Wheels in Place. — In April, 1903, a Leffel turbine 
was tested at Logan, Utah, at the station of The Teiluride Power 
Transmission Company, by P. N. Nunn, Chief Engineer. The 
wheel was dir^ectly connected to a General Electric generator the 
efficiency of which has been determined as follows : 

125 per cent load 96. 7 i>er cent, efficiency 

100 per cent load 96.2x)ereent. efficiency 

75 per cent load 95.3 per cent efficiency 

50 per cent luad..... 98.5x>ercent. efficiency 

25 percent load 88.0i>er oenk efficiency 

The output of this generator was used as a basis for calculating 
the work done by the water wheel. 

The results of the tests and methods of calculation are shown in 
Table XXXV and graphically illustrated in Fig. 234. 

TABLE XXXV. 

Tht of High Head Liffel Horizontal Turbine at Lagan StoMon of Telhirids 

Power Trans, Company^ Logan^ Utah, Efflciencif of Teat at Constant Speedy 

AprU £8,1905. 

P. N. Nunn, Ohief En^neer. 



Grate opening 


0.75 
1.394 

81.85 

0.85 
1.98 

80.72 

86.5 

199.3 

10.4 
209.7 
1921 
1152 

0.965 
1600 
0.833 
0.75 


0.50 
1.132 

59.76 

0.85 
1.98 

58.63 

87.3 

201.2 

10.6 
211.8 
1409 
739 
0.952 
1041 
0.738 
0.50 


0.40 
0.969 

47.27 

0.85 
1.98 

46.14 

87.5 

201.6 

10.8 
212.4 
1112 
500 

0.935 
717 
0.644 
0.40 


0.50 
1.129 

59.66 

0.85 
1.98 

58.63 

87.2 

200.9 

10.6 
211.5 
1405 
737 

0.952 
1038 
0.739 
0.50 


0.75 
1.368 

79.65 

0.85 
1.98 

78.42 

86.5 

199.3 

10.4 
209.7 
1866 
1123 

0.965 
1560 
0.836 
0.75 


96 


^ead on 1& feet weir in feet 

^^harge of weir in cubic feet 

Der second 


1.475 
88.94 


^^eakage around weir in sec- 
ond feet 


0.85 


Bzciter water in second feet 

VVater through turbine in 

second feet .• . 


1.98 
87.81 


Pressure at shaft center in 
pounds per square inch. . 

Elffective head above shaft 
renter in feet 


86.2 
198.6 


Vacuum head measured in 
feet 


10.3 


Total working head in feet 

rheoretical horse power 

C. W. output at Sw. Bd 

Jenerator efficiency 

Jrake horse power of turbine 

^ciency of turbine 

rat*» ooenins 


208.9 

2082 

1210 
0.967 

1677 
0.806 
0.96 







NoFB— Speed. 400 R. P. M. (normal). 

Generator efficiency taken from test of machine made by The Greneral Electric 
ompany. (Record of test in office of chief engineer). 



38o 



Turbine Testing, 



A similar test of one of a number of wheels installed by Tlie 
James Leffel Company in the plant of the Niagara Hydraulic 
Power and Manufacturings Company was made in December, 1905, 
by Mn John L. Harper, engineer of that company. The following 
table XXXVI is the condensed data of the test of wheel No* 8 
which is also illustrated by Fig. 235, 



9400 

a too 

auQQ 
eiDo 
eeoo 



yi£40a 



BBOO 

oeo6o 
imo 

IBDD 
1400 
1200 
IDOO 



- 00 

■ 00 

■ 71 
' 70 

- 00 

yiO 
u 

ae 
w 

5" 

IL 

liflO 












- 










^ 




ITS 
llOo 








y 


^ 










^^ 


-- 








/ 


/' 






y 


y 













^/ 


/ 






/ 


/^ 


^ 










71 


jf 






/ 


/ 


/ 












ICO t 






/ 


\/ 


/ 














/ 




J 


¥ 


/ 
















100 o 

■0 

■b| 

TOO 
00 

so 






f 


/ 


/ 


















/ 


i 


f 




















/ 


/ 


^/ 


/ 


















' 11 

^ 10 

- tl 


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7 






















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/ 






















i 


( 























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i 



40 46 so 19 10 OS 70 7S 00 99 SO 19 
pen GCHT SATE OPCMlMa 

Y\t^ 235. 

The water was measured by a standard contracted weir 16.25 
feet long and discharge computed by Francis* formula: 

q==3.33{L— 0.2h) h* 

The load was computed from the voltmeter and ammeter rca<l- 
ings of two generators Nos, 5 and 12 which were both driven by j 
this wheel and then corrected for the generator loss by a fact<:j 
estimated from the shop tests of the generators. 




Wheels io Place. 



TABLE XXX VL 

T€*t of a Douhh Horhfmtal Leffet Turbine ijtst ailed in the plant of the 

Niagarn Ui/drauHc Company, Niagara Fa 11% N, F, 



Gatk Ofxkhto. 



.45 



Dec. 5th 



Time -,,,,,.....* , . . 

Hook gauge reading (corrected) 

rHscharge of wheel by Francia* formula . 

Hc^ad on turbine .,-,.. 

lEydraulic horse power* » .«,,,,,.* . 

r;f- M,*- .,... 



Gen f rat or No. S* 

Volta_...„. ..,.-..., , 

Amperes. , , , , , , 

Efficiency 

HorEe power taken frora wheel by generator. . . . 

Gftieratar No. 12*^ 

Volta , ...„,. 

Amperes ,.,...... , » , . 

Effciency . , , . ^ > , , 

Horse puwer talcen from wheel by gt^nerator 

Total horse power output of wheel ,..,., 

EfSciem-y of wheel ........,...,,, , . . 



3;2l p- m. 

1,3155 

84.76 

213.0 

2045 

255 

178 

5065 

1314 

Friction 
Load 
Only 
17 
1331 
,fi5l 




5:01 p, m. 

1.978 
146.6 
212.4 

S52S 
259 

178 
5020 

.92 
1302 

12200 
57.7 
.1*5 
1720 
3022 
.So6 



fDOQ 



4QQ0 



saoa 
Fig. 236, 



lODQ 



lODIP 



4:59 p. 1 
2.2.57 

17S.3 

212.7 
4320 
250 

184 
5S33 

.92 
15^3 



13000 
60.5 

.955 
1912 
3475 
.Ra5 




leaQi 



• Generator No, 5 is a G. B, 5000 A. 175 V., D. C. tnachlneu 

•• Generator No. 12 is a Bullock 1000 K. W„ 3 phase A C. senerator. 





Turbine Testing, 

The 10,500 h.p, turbine manufactured by the L R Morris Com- 
pany for the Shawinigan Power Company was also tested in a 
similar manner. A brief outline of this test is given on page 416 
The graphical result of the same is shown by Fig, 236. Fig. 237 
illtistrates the test of a 25" Victor High Pressure Turbine, manu- 
factured by the Piatt Iron Works Co*, at the Houck Falls Power 
Station at Ellensville, New York, 

The results of various tests at the Holyoke Testing Fluniep zd^ 
lected from divers sources^ are given in the appendix. Most of ik 
later tests have been furnished by manufacturers and represeat the 
best results of modern turbine manufacture. 




mo 40D 100 •DO loog ibdd 1400 iioo ibod eoos itOQ i4oa 



Fig, 237- 




Literature. 383 



LITERATURE. 

TUBBINB TESTINO. 

1. Smeaton, James. "An Experimental Inquiry, read in the Philosophical 

Society of London, May 3rd and 10th, 1759, concerning the 
Natural Powers of Water to Turn Mills and Other Machines, 
Depending on a Circular Motion." 

2. Morin. "Experiences sur lea Power Hydraulicques." Paris, 1838. 

3. Pourneyron, H. "Memoire sur les Turbines Hydraulicques." Bnussels, 

1840. 

4. Francis, J. B. Tests of Several Turbines Including the Tremont-Fourney* 

ron and the Boott Center Vent Wheels. Lowell Hydraulic Ex- 
periments, 1847-1851. 

5. Francis. J. B. Test of Humphrey Turbine, 275 h. p. Trans. Am. Soc. 

C. E.. vol. 13, pp. 295-303. 1884. 

6. Webber. Samuel. Turbine Testing. Elec. Rev. Oct 18. 1895. p. 477. 

7. Wiebber, Samuel. Instructions for Testing Turbines. Eng. News, 1895. 

Vol. 2, p. 372. 

8. Cazin. F. M. F. The Efficiency of Water Wheels. Elec. Wld. Jan. 9, 1897. 
S. Report of Tests of a 28-inch and 36-inch "Cascade" Water Wheel. Jour. 

Fr. Inst May, 1897. 
10. Hitchcock, E. A. Impulse Water Wheel Experiments. Elec. Wld. June 

5, 1897. 
U. Hatt W. Kendrlck. An Efficiency Surface for Pelton Motor. Jour. 

Franklin Inst, June, 1897, vol. 143, p. 455. 
^2. Thurston. R. H. Systematic Testing of Turbine Watei* Wheels in the 

United States. Am. Soc. Mech. £!ng. 1897, p. 359. 

13. Results of Tests of Cascade Wheel. Eng. News, 1897, vol. 2, p. 27 

14. Results of Tests of Hug Wheel. Eng. News. 1898, vol. 2, p. 327. 

15. Efficiency Curves. Eng. News, 1903, vol. 2, p. 312. 

18^ Houston. W. C. Tests with a Pelton Wheel. Mech. Engr., May 30, 1903. 
n. Henry, Geo. J., Jr. Tangential Water Wheel Efficiencies. Am. Inst Elec. 

EIng., Sept 25, 1903. 
IS. Crowell. H. C. and Lenth. G. C. D. An Investigation of the Doble Needle 

Regulating Nozzle. Thesis, Mass. Inst, of Tech. 1903. 

19. LeConte. Joseph N. Efficiency Test of an Impulse Wheel. Cal. Jour, of 

Tech. May, 1904. 

20. Groait, B. F. E^xperiments and Formula for the Efficiency of Tangential 

Water Wheels. Eng. News, 1904, vol. 2. p. 430. 

21. Webber, Wm. O. Efficiency Tests of Turbine Water Wheels. Am. Soc. 

of Mech. Ehigrs., May, 1906. 

'2. Horton. R. E. Turbine Water Wheel Tests. Water Supply and Irriga- 
tion Paper 180, 1906. 

}. Westcott. A. L. Tests of a 12-lnch Doble Water Wheel. Power, Dec 
1907. 



CHAPTER XVI. 



> 



THE SELECTION OF THE TURBINE, 

182* Effect of Conditions of Operation.^-For high and moder- 
ate falls the variations in head under different conditions of limtr 
are of small importance and water wheels can commonly be 
placed high enough above tail- water to be practically free from 
its influences. In such cases variations in head are comparaiivclj 
so slight as to have little eflfect on the operation of the wheels 
which can therefore be selected for a single head. Such condi- 
tions are the most fa%^orable for all types of wheels. 

When low falls are developed the rise in the tail-water is oftcB 
comparatively great, and, as the head water cannot commonly 
be permitted to rise to a similar extent on account of overflow] 
and damage from back water, the heads at such time are consider- 
ably reduced. As is pointed out in Chapter V, under such con-| 
ditions and for continuous power purposes wheels must be se* 
lected, if possible, that will operate satisfactorily under the eniirci 
range of head variations that the conditions may demand, or at, 
least under as great a range of such variations as practicable- 

In some cases the change in head is so great that no wheel cat] 
be selected which with work satisfactorily under the entire rangej 
of conditions. In other cases, the head becomes so small that 
the power which can be developed is insufricicnt without a ht\ 
and unwarranted first cost. Jn many such cases the use oi 
water power plant must be discontinued, and, if the deliver}' 
power must be continuous, it must be temporarily supplement! 
or replaced by some form of auxiliary power. 

In Chapter XVII it is shown that^ almost without exceptu 
great variations take place in every power load and that a pbi 
must therefore be designed to work satisfactorily under consid< 
able changes in load. Most plants are called upon to (umii 
power for a considerable portion of the time under much lei 
than their maximum load, hut must occasionally furnish a ni; 
mum load for a short period. 




Basis tor the Selection of the Turbine. 385 

If power IS valuable, and the quantity of water is limited, it is 
desirable to select a wheel that will give the maximum efficiency 
for the condition of load under which it must operate for the 
greater portion of the time and that will also give, if possible, 
high efficiency under the head available at the lowest stages of 
the water. High efficiency is not essential to economy during 
high water, for there is plenty of water to spare at such times; 
neither is high efficiency as important during unusual load con- 
ditions, which obtain for only brief intervals, as it is during the 
average conditions under which the plant operates. 

183.. Basis for the Selection of the Turbine. — In Chapter XV 
the testing of water wheels has been discussed and a number of 
tabulated results of such tests are given. (See appendix D). The 
standard water wheel tables are calculated from the results of 
these tests but the values of power and efficiency, as given therein, 
are usually reduced somewhat for safety from the results deter- 
mined experimentally. Such tests also give data for a much 
broader consideration of the question, and for the determination 
of the results that can be obtained under the actual conditions 
of installation and operation, even when such conditions are sub- 
ject to wide variations. 

In Chapter XIV the hydraulics of the turbine are discussed, 
various turbine constants are considered, and the constants are 
calculated for a number of standard American turbines in accord- 
ance with the conditions of operation as recommended in the cata- 
logues of their makers. It will be seen from a study of the tables 
that the turbines designed and built by various manufacturers 
Sometimes have widely different constants, indicating that each is 
l>est adapted to certain conditions of which the values of these 
Constants are an index. 

It is also shown that the various constants for a homogeneous 
Series of wheels may be calculated from experimental data for 
iny desired condition of gate opening and fixed value of <f>, and 
ihat from these constants the operating results, that is, the dis- 
charge, power, speed, and efficiency for any wheel of the series, 
^ith the given gate opening and value of <^ and for any desired 
lead, can be calculated. For most purposes, where the head is 
constant or where the range in heads and other conditions to be 
ronsidered are not extreme, the necessary calculations can be 
eadily made from a satisfactory test, by applying some of the 



386 The Selection of the Turbine. 

formulas developed and discussed in Chapter XIV. The forraih 
las of greatest value for this purpose are as follows: 

, D n 

1 q> = r^ 

1842V h 

^ 1842 <P , , ^ 

2 ni= — g— , when h =s 1 

Dn _ D, n, , 
S A = -7== w^ when <p 10 constant. 

4 -y== = -7= when q> and D are constant. 

^^ • 

5 n = n , i^h when <p and D are constant. 

q Qi 

7 -7== = --r== when <p and D are constant. 

8 q = Qi "^h when (p and D are constant. 



10 



-7-5- = -TT when <?) IB constant, 
hi lilt 



11 P = P h' when (p and D are constant and hi = L 

In using these formulas it must be remembered that each i^ 
essentially correct only when the condition specified after each 
equation obtains; also that as long as </> remains constant the 
efficiency obtained by the test will remain practically constant 
for the same wheel, under all conditions of head. It should aba 
be noted that, with a fixed diameter of wheel and a fixed head, ♦ 
and n are in direct proportion, and most calculations can be made 
by a direct consideration of the values cf n without a determina- 
tion of the value of <f>. 

When the operating results are calculated for a wheel of a given 
series but of a diameter differing from that on which the experi- 
ments were made, the results are liable to differ from the true 
results on account of variations in manufacture, and allowance 
must be made for such differences, at least until the art of manth 
facturing turbines has further advanced. 



urbme tor unti 



leac 



P 184- Selection of the Turbine for Uniform Head and Power.— 

X he conditions of operation, as catalogued, 'are usually based upon 

tests of a few turbines oi the series, and represent the best coo- 

ciitions of operation for that series of wheels as determined by 

such tests. Where the conditions of installation and operation 

are fixed, and are not subject to radical changes in head or to great 

x-ariations in the demand for power, the selection of a wheel may 

tie made by inspection directly from the catalogues. This method 

of selection is based on the assumption that the catalogue data is 

correct, which assumption should be verified by the records of 

an actual test of the series of wheels and, if possible, of the size 

and hand which are actually to be used. 

The examination of the many catalogues of turbine manufactur- 
ers, in order to determine the wheel best suited to the conditions, 
is a tedious method of procedure and can be greatly shortened by 
brief calculations which are described in the following sections: 

i85. The Selection of a Turbine for a Given Speed and Power 
to Work under a Given Fixed Head. — It is frequently necessary 
to select a turbine which must have a given speed and power in 
order to successfully operate machinery for v'*Mch such require- 
ments obtain. It is desirable to select a wheel which will furnish 
essentially the amount of power required as all machinery will 
work more efficiently and more satisfactorily at or near full load 
conditions. It is also desirable to use a single turbine rather than 
two turbines, and if more than one turbine is required, the least 
number found practicable should usually be selected because the 
multiplication of units involves an increase in the number of bear- 
ings which must be maintained and kept in alignment. 

To determine the best installation of turbines necessary to ful- 
fill the given conditions, the value of K^ as given by equation (12} 
should be determined. Having determined the value of K^, a 
turbine should be selected having a constant Kb not less than the 
amount determined, and if it is desired to operate the turbine at 
its maximum efficiency, the value of K^^ for the turbine selected 
should not greatly exceed the value found by computation. If 
the value of Kq as computed greatly exceeds the value of Ks for 
the various makes of turbines, then the power must be divided 
between two or more units in order that the conditions may be 
satisfied. As K^ is in direct proportion to P, one- half, one-third or 
any other fraction of K^ will give the value of K, for a wheel 
having a similar fractional value of the power, P, atid will there- 



388 The Selection of the Turbine. ^^^^m 

fore show the type of wheel which must be selected in order that 
two, three, or more will do the work in question. The great vam- 
tions in the value of K^ for different types of wheels and the in- 
fluence of this variation on the relation of speed and power will 
be seen by reference to Fig, 222 which shows the curves of r^ 
lation between revolution and power of various wheels for mt 
foot head. This may be used for any other head by considering tk 
revolutions in proportion to the square root of the head and the 
power in proportion to the three-halves power of the head* A 
brief study of this diagram will show its use more plainly. For 
example : under a one foot head, and for 30 revolutions per minuU, 
turbines may be selected that will deliver from 1*3 to 6.6 horse 
power. 

Suppose we desire to determine the power that wil! be available 
under a 16' head at 100 revolutions per minute, 100 revolutions 
per mintite at 16' head would correspond to 25 revolutions per| 
minute at i' head. 

For since 

vr 

therefore n^ = -7= 100 = .25 X 100 = 2S. 
vlti 

At 25 r. p, m. the diagram shows that turbines are obtainable j 
that will give 1,8 to 10 horse power at one foot head. 

The power at 16 foot head will be to the power at one foot head 
as the three-halves power of the head. The three-halves power of 
16 is 64; hence the power at 16 feet will be 64 times the power at 
one foot head, and, hencCj wheels under a 16 foot head operated ai 
100 revolutions per minute, will furnish from 122 to 657 horse 
power and the most satisfactory wheel within these limits far Llic 
problem at hand can be selected. 

The diagram, however, is a convenience, not a necessity, and a 
problem can often be more readily solved by the direct applica- 
tion of equation 12. If, for example, it is desired to operate a 
turbine at 100 revolutions per minute under i6 foot head to de- 
velop 400 h. p., the corresponding value of K^ will be 

n»P 100 X 100 X 400 ^^^ 
K, = -7= = 7^^ = 5906 

By examination of Table XXXII it will be found that the Victor! 
Standard Cylinder Gate or the United States Turbine wheels havtl 




To Estimate Probable Results From a Test. 389 

radically this value of K^ and will therefore fulfill the conditions, 
laving determined from the calculated value of Kj the makes and 
fpts of the several wheels which will satisfy the requirements, the 
ize of the wheel may immdiately be determined by determining 
he value of K, for the same series of wheels from Table XXX, 
lap. XIV, and calculating the size of the wheel by the use of for- 
lula 9. 

Thus for the Victor Standard Cylinder Gate wheel the value of 
C, is 0.00205. Therefore from equation (9) 



^ = ^ = ^ 



^ =56.2- 



.00205 X 64 
vhich is the size of this series of wheels needed to fulfill the as- 
umed conditions. 

Having thus selected several possible wheels, tenders for these 
vhccls may be invited from their makers. These tenders should 
ic accompanied by an official report of a Holyoke test for the 
wheel in question, or, if this is not available at the time, for the 
acxt larger and the next smaller wheels of the series which have 
^cn tested. From these tests the catalogue values of Kj and K5 
which were used in their selection can be checked. In addition 
^0 this the several prospective wheels may be compared as to their 
operation at part gate, which comparison is equally important 
for the final choice to be made. 

As the wheels are seldom or never tested for the head under 
which they are to work, and as tests are not always available for 
-he size of wheel to be used, it is necessary to predict from the test 
^ata furnished by the wheel makers the efficiency, power and 
^ater-consumption curves which can be anticipated under the 
f'vcn head. This can be done as illustrated in the next two 
tides. 

X86. To Estimate the Operating Results of a Turbine under 
lie Head from Test Results secured at another Head. — ^For the 
iirpose of illustrating the methods of calculation. Table LXXIII. 
ay be considered. This table gives the results of certain tests 

a 33* special, left-hand turbine wheel, with conical draft tube 
Id balance gate, manufactured by the S. Morgan Smith Com- 
Uiy. While the heads in the different experiments of this test 
iry slightly, they are so nearly uniform that the table may be 
■nsidered as developed under a uniform head of 17.15 feet. If 
eater accuracy is desired, however, the square root of the actual 
ad can be considered each time. 



39^ 



The Selection of the Turbine. 



Let it be assumed that the wheel is to be operated under a ao 
foot head and with a speed of 200 n p* m. with the average load 
at about .765 gate. The maximum efficiency at .765 gate is ^epr^ 
sen ted by experiment No. 43 of this table* In order that tfai 
wheel shall work under the new head with this efficiency, equaticm 
(4) must be satisfied. In all of these equations the primed cliaf* 
actcrs are used to represent the experimental conditions* Tbf 
most efficient revolutions under the tiew head will therefore be 
determined as fallows: 



172.75 X 4.46 
4.14 



= 186 f* p* m. 



The wheel to be chosen must, howeveri in this case operate it 
200 revolutions per minute. At 200 r. p. m. the wheel will i!Ot 
run at its maximum efficiency* The actual efficiency at this sp«d 
may be determined by finding what speed at the e^erimerittl 
head corresponds with the speed to be used, and notin|f the ei 
ciency corresponding to the same. This is done on the asstnn) 
tion that the efficiency remains constant as long as ^ remri 
constant which is shown to be essentially true by Fig, 214, 
XIV, 

The revolutions under 17.15 ft. head corresponding to 200 r 
p. m, under 20 feet will be determined as before: 

200 X 4.14 



n' = 



4,46 



' = 187 T. p. m. 



The result, 1S7 r. p, m., lies between the conditions of exp 
ments 41 and 40, By proportion, the efficiency corresponding Ml 
187 r p. m. will be found to be about ^.25 at ,765 ^^te. 

If the efficiency corresponding to 187 r, p, m, in the table is no 
determined from each g^te opening, it will be found that at full gat^i 
the efficiency will be slightly below that shown in experiment tS«| 
and can be determined by interpolation, or graphically, £0 ^\ 
About 81%, At gate ,948 the efficiency can be determined In ! 
same way to be about 8275%. At gate .883 the results will 
between experiments 69 and 70 and the efficiency will be found 1 
he about 86% » At gate .851 the result falls below experiment 
and, by calculation from a graphical diagram or by interpolatioi 
the results are found to be about .86. At gate 702 the rcvduti<^ 
correspond closely with experiment 56, and the efficiency from' 
table is found to be 81,35%. At gate .636 the revolutions f.Mt I 
tween experiments 25 and 26 and, by proportion, the efficiency 



L 



iilL. 



Effects of Diameter on Results. 



39» 



found to be 80.62%. At gate .556, the efficiency is found, by pro- 
portion, to be 77%. To determine the power of the wheel under 
the new conditions, and for each condition of gate, the power of 
the wheel as found by the test must be determined for the same 
value of ^. The power of the new head can then be calculated by 
use of formula (11). 

In the same manner the discharge of the turbine can be deter- 
mined by finding the value of q corresponding to the value of ^ 
for the experimental head, and from this value so determined the 
value of q under the 20 foot head can be calculated by formula (7). 
The results of these calculations, together with the efficiency as 
determined for 20 foot head and for 200 revolutions per minute, 
are given in Table XXXVII. 

Having computed a similar table for each of the several pros- 
pective wheels the one best suited to the given conditions can be 
chosen. 

TABLE XXXVII. 

9mring H^ru Power, Ditekarge and Efficiency of »ineh Speeial Uft Ecmd 

8. Morgan Smith Turbine, wUh tChfoot head and tOO R P. ML 

OUcoUtfid from lest of dMuch. wheel under a head of 17.15 feet 



Proportional Gate Opening. 


Horse Power 


Discbarge, 

cubic feet 
per second. 


Efficiency. 


i.ooo 


222.1 
220.1 
217.7 
212.7 
188.1 
165.1 
154.7 
136.7 


120.4 

117.0 

111.3 

109.2 

97.5 

87.8 

81.5 

75.0 


81.6 


.948 


83.2 


.883 


85.6 


851......... 


86.8 


.7ft5 


88.2 


.702 


81.8 


.©6 


80.7 


.556 


79.0 







187. To Estimate the Operating Results of a Turbine of one 
Diameter from Test Results of Another Diameter of the Same 
Series. — It is always desirable for the purpose of calculations to 
Use the results of a test made on a wheel of the same size and hand 
^ that which is to be used in the installation for which the wheel 
is being considered. It is seldom, however, that all of the various 
lizes of wheels in a series of wheels have been tested, and the 
Manufacturers therefore frequently base their estimates and guar- 
mtees of wheels of an untested size on the test of some other 
vhcel of the series which may be larger or smaller than the whee' 



i 



i 






392 ■ The Selection of the Turbine, 

offered* Sometimes tests of wheels both larger and smaller thm 
the wheel to be used ate available, in which case both sets of tests 
should be used as a basis of calculation. 

Let it be assumed that a 40" wheel is to be installed of the same 
series as the 33'' wheel just considered, and that no tests of such 
a wheel are obtainable. The tests of the 33" wheel may thercfort ! 
be used as the best information available* Let it be assumed thai 
the 40" wheel is to be operated under a 9 foot head* For these J 
calculations formula (3) must be satisfied. 

Let it be assumed that the wheel is to operate at nearly full load 
and the best efficiency is desired at about .85 gate. From the tests it I 
will be found that at .85 gate, and with a 17,15 foot head and 191 J 
revolutions, the wheel gave 85.97% eflSciency and 170,08 horse 
power. Substituting these values in equation (3) there results: 

— ^-j^ — = g , from which n = 114 r. p. m. 

One hundred and fourteen revolutions per minute is therefore 
the speed under which the wheel must operate in order to give 
this maximum efficiency at this gate. 

Let it be assumed, however, that the wheel must be run at i^ 
n p. m., on account of the class of machinery to be opentd 
By substituting the value n^i20j in equation (3)/ 't is found 
that n' = 202. The experimental efficiency at 202 n p- m. under 
the 17*15 foot head and with the 33" wheel, will therefore* corres- 
pond to 120 revolutions tinder a 9 foot head with a 40" wheel and 
will indicate the efficiency under which the wheel will operate under 
these conditions. Tliis is found to be about 81.5 at ,85 gate. 

In order to determine the horse power of the wheel under the 
new conditions, the horse power of the wheel under the test con* 
ditions must first be determined for that gate; the resulting horse 
power can then be determined by equation (9), 

For 202 r p. m. at 17J5 foot head for this 33* wheel ?=B 
which, substituted in equation (g), gives 

S3 X 33 X 71 - 40 X 40 X 27 ^^^^ ^^^^^ P -^ 88. 

In the same manner, the discharge of the larger wheel under the' 
lower head can be determined by equation (6)* and q is found tt> 
equal 104 cu. ft. per second. 




To Estimate Results with Variable Heads. 



393 



I this way the discharge, efficiency and power of the larger 
el under the chosen r. p. m. can be determined for each condi- 
of gate, as shown in Table XXXVIII. 

TABLE XXXVIII. 

Hng Horse Potcer^ Discharge and Efficiency of a 4Mnch Special Left Hand 
S. Morgan Smith Turbine, with a 9-Joot head and ItO R P. M. 
Calculated from test of 3d-inch wheel under a head of 17.16 feet. 



Proportional Gate Opening. 



Horse 
Power 



Discharge 

cubic feet 

per second. 



Efficiency. 



) 

I 
> 
I 
3 
5 



100. 
100. 

92. 

88. 

76. 

68. 

64. 

58. 



119. 
112. 
108. 
104. 

91. 

83. 

76. 

73. 



82.1 
84.2 
82.5 
81.5 
78.1 
77.8 
78.8 
75.1 



J8. To Estimate the Operating Results of a Turbine imder 
iable Heads from a Test made under a Fixed Head. — ^Where 
variations in the head under which a wheel is to operate are 
siderable, the variation in <^, and consequently in n, are some- 
5S found to be beyond the limits of the test. Where the test 
ditions are not greatly exceeded, the experiments may be ex- 
ied graphically without any serious error. 
,et it be assumed that the 33" wheel above considered is to be 
rated under a maximum head of 25 feet, and that the head will 
rease to 16 feet at times of high water; also, that the wheel is 
be operated for the major portion of the time under about .75 
e. The best condition for operation is shown by test 43, which 
ws an efficiency of 86.3% at n'= 172.75 r. p. m. 
may be calculated from equation (4) for the 25 foot head as 
ows: 

172.75 X 5 ^^^ 
n = jj^ = 208 r. p. m. 

It is : the best number of revolutions for a 25 ft working head 
lid be 208 r. p. m. The best number of revolutions for a six- 
i foot head would be determined as follows: 



n = 



172.75 X 4 

4.14 



= 166 r. p. m. 



24 



394 



The Selection of the Turbine. 



I 



The wheel, for the best efficiency, should be run at a different 
speed for each head, but under practical conditions of semce 
must be run at a constant speed. 

Let it be assumed that, on account of the machinery operated, 
it is desirable to adopt for the plant a speed of 200 r, p* m. Let 
the 25 foot head be first considered. For considering the 25 foot 
head the equivalent value of n under the test conditions is foiin^ 
as follows; 

n'= a»X4.14 ^ 167 r. p. 01. 
5 

It will be noted from experiment 44 that at 169.25 r, p, m. the 

efficiency is 85,55, A* 167 revolutions per minute tbe efficieoqr 

would therefore be about 85%. Under a sixteen foot head n must 

also equal 200 r. p, m., hence^ for this case^ the equivalent value of 

n' for the test conditions is 

^,^ _200X4a4_ ^ 208 revolutions. 
4 

Test 39 shows that, with 206.25 revolutions, the efficiency 
76,66, At 208 revolutions the efficiency is therefore less than thil 
amount and the probable efficiency under these conditions cao 
be estimated by platting the relation between revolutions and tUm 
ficiency as shown in Fig, 238. By prolonging the line from tJii 
actual experiments, the efficiency indicated for 208 revolutioi 
under the experimental condition s^ is found to be about 76' 
As far as efficiency is concerned, therefore, the arrangement is v^ 
satisfactory, for a sufficiently high efficiency will be obtained ««* 
der conditions of high water, and when the quantity of water tis< 
is immaterial. 

The relations of efficiency to speed, under the experimental coft-| 
ditions and at various gate openings, are shown by the poii 
platted on Fig, 238, Through these points mean curves ai 
drawn, which are extended where necessary to intersect tfie i 
scissa of 167 revolutions, which corresponds to the condition 1 
efficiency for 25 foot head, and to the abscissa of 20S revolui 
which corresponds to the condition of efficiency for a 16 foot 
From these results the relations of efficiency at various gates 
at the two heads named are platted in Fig, 239. 

The relations of power to speed are shown by Fig- 240, whi£ 
has been platted in the same manner as Fig. 238, From Fig* 



Estimate of Efficiency with Variable Head. 



395 















^^ 






dH^^a 
















w 






b 


!^ 


^ 


^ 


f*'-^ 


^ 


\ 




—K 














J. 


^ 


3 


r^ 


h 




ir 


N 




r 


V 






^ 


^"'^ 




1-^ 

1 


jxa 






:^ 




^ 


\ 


^ 


> 


\ 








■+- 


^ 










^ 


!&v 


^ 




-" — ( 


\ 


\ 
















^^ 




-as, 


£i*h. 


^ 


"v 

s 




C'l" 


\ 


\ 








9 














-S3It 




J 




^ 




V 








s 

X 

1- 


















3 




"^ 


N 


$ 








s 


















m 








N^ 




U 











It 

lev 




(urrtDi 


II nfi 


uiiu 


«,« 


ID 








n 


ID ^ 



238. — Curves Showing the Efficiency Obtained at Various Speeds un- 
der a Test Head of about 17.15 Feet from a 33-Inch Special Left- 
Hand Wheel with Balance Qate, Manufactured by the S. Morgan 
Smith Co. 













i>A 




A 


V 






^ 


^ 






p^ 


L 


/ 


\ 




1 _ n 1 ♦> 


f 


r 










^ 


\ 




.A 


X 














"^ 




• 










> 


70 










. o 


IB FO 


JTHEA 


D 


^ 














^ 


























































•a' 


« 


Q 


7 
PER C 



CNT 6i 


8 

fkTE or 



>CNIHC. 


9 





101 



239.— CuFYes Showing Estimated Efficiency at Various Gate Openings 
and at Two Heads for 33-Inch S. Morgan Smith Wheel. (Taken 
from Fig. 238.) 



39*5 



The Selection of the Turbine, 



the power of the wheel at 25 and 16 feet can be determined by 
equation (10). 
The power at 25 feet will be 

h* 12s 

— I = ^g-g = 1.77 liraes Ibe power determined by theeiper 

^' ' imeiit at 17.15 feet aud 167 r* p, m* 

The power at 16 feet will be 

b* 64 

— I =£ =g-g = ,91 timed tbe power, as determined by the ei» 

^' * peri men t at 17,15 feet, and at 216 r. p, m. 




I 



leo eoa 

hEVQuniDHS nn minutc 

Fig. 240.— Curves Sbowlng th© Power Obtained at Different Speeds uflder » 
Test Head of about 17.16 Feet from the S, Morgan Smith 
33-rDcb WheeL 

.91 times the power, as determined by the experiment at 17.15 f«t*j 
and at 216 r, p, m. Curves of the power of this wheel under 25 u^M 
16 foot heads, and at various gates, as determined in this irianner," 
are shown by Fig. 241 

The experimental relations of speed and discharge for the wl 
are shown in Fig. 242 which was platted in the same manner 
the diagrams for efficiency and power. A graphical represenU- 
lion of the discharge under 25 and 16 foot head and at vari< 
gates is shown in Fig. 243 

1 89. A More Exact Graphical Method for CalculatioiL— -' 
method outlined in section 188 is subject to some error as iht 
suits arc platted regardless of head. The graphical method 
therefore applicable without correction only when the experimd 



A Graphical Method of Calculation. 



397 



head remains nearly constant. For a more complete^ accurate 
1 satisfactory analysis the discharge, power and revolutions 
)uld be reduced to their equivalents i. e. at one foot head 



qi = 



i/iT' 



Pi = 



hj 



n 



m 



»o 



!80 



'80 



140 



too 



















, 


1 










• 

%1 


;i^ 
















^ 


^ 


















f/ 
















f' 


r 


















/ 






















































> 


















♦5^ 


/ 














,A^* 


^ 


^' 












te 


t^ 


p. 




























\ 


90 


8 


D 


7 
PCR C 




CNT 6i 


8 
Kit Of 



'CNIN8. 


8 





m 



f. 241. —Curves Showing Estimated Power Obtained at Various Gate 
Openings and at Two Heads for 33-Inch S. Morgan Smith WheeL 
(Taken from Fig. 240.) 

I platted as shown in Fig. 244 where the r. p. m. under one foot 
id is used as abscissas, and the power, discharge and efficiencies 
used as ordinates. The condition at any given number of 
olutions under a given head can be calculated by dividing the 
•n number of revolutions by the square root of the head. The 



398 



The Selection of the Turbine, 




ISO eoo 

nCVOLUTIONS WEM ynHtftt 



Fig. 242.— Curves Showing the Discharge at Various Speeds under tteTMtl 
Head of about 17.16 Feet oC Uie 33-Iiich S, Morgan Smith Wh^l 



140 




















^ 


X 

o 
u 

LJ 














^^ 


fk^ 


^ 














*J^ 


^ 
















i 


f 


1 






f^ 




^ 


D 
(-1 




^ 


/" 








,/ 


> 










y 






jh 


y 


/ 








5 sn- 

1-3 

m 






\« 


<^ 


^ 












BO 




'r^ 
















SO 


e 





7 


D 


a 





9 


a 


li 



pen CCNT SATC 0PCW1I6 

Fig. 243* — Curves Showing the Estimated Discharge at Various Gate Op" 

lugs and at Two Heads for the 33-Iiicli S. Morgan Smitli Wfa 

Taken from Fig. 242J 



^^^ A Graphical Method o£ Calcuiaiion. 399 1 


w 

80 
76 
72 

I 

i 
.2.0 

J 

1 

\ 

14 

i 

i" 

! 
'24 

• 411 




1 




































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bO»iN 






















rr^ 


r-^ 


>S 


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te: 


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1 3a 40 42 44 48 46 5Q 52 54 

RPM UNDER DNC FOOT HEAD. 

244.— -Curves of the 33-1 uch S- Morgan Smith ^bee\ tot Oiie VoQlU^sj&i 


V^ 



400 



The Selection of the Turbine, 



result is the comparative revolutions under one foot head, and a 
line drawn vertically at the point so located on the diagram will 
give the basis of calculations for power and discharge by muJti* 
plying by hi and h^, respectively, for each gate opening and by 
reading the efficiency direct. 

For the wheel under 200 revolutions at 25 and 16 foot heads the 
etjuivalent speeds on the diagram are 40 and 50, respectively, 
Lines drawn vertically at these points will intersect the curves oi 
efficiency, power and discharge and if reduced by a similar method 
will give curves essentially the same as those shown in Figs, 239, 
241 and 243. This is probably the best method for common use 
in studying, from test data, the operation of a wheel under a 
riable head. 

190. The Construction of the Characteristic Curves of a Ter- 
bine. — It is frequently desirable to make a more thorough analy- 
sts, based on the available test, of the conditions under which 1 
wheel can operate* For this purpose, the writer finds the use 
what he has termed "the characteristic curve" o^ a turbine to he 
the most comprehensive method for such an analysis* 

For this purpose, prepare a diagram on which the ordinate^ rep- 
resent the values of <^ and the r, p, m. under one foot head, ad 
the abscissas the discharge of the wheels in cubic feet per second 
under one foot head. It is also found desirable to show on the 
upper margin of the diagram the horse power under one fo<^^ hea4 
with iao% efficiency, corresponding to the discharge shown below. 
For each experimental result the values of <p and of the discharge 
under one foot head are determined by formulas (l) and {])* 
The point representing these values is then platted on the dts- 
g^ram, and the efficiency, as determined by the test for that exp^n- 
ment, is written closely adjoining the platted point. This is don^ 
for each experiment at each condition of gate. After all the cX' 
perimental points are platted^ and the resulting efficiency at each 
given point is expressed, lines of equal efficiency are interpolitrf' 
on the drawing, and will indicate the general law of the variation 
of efficiency as represented by the test 

It is, of course, possible to reduce the horse power determine 
for each experiment to the theoretical horse power under one f< 
head, and record it at the corresponding point, and then interpolate^ 
horse power curves, as in the case of the efficiency curves. It 
been found by the writer, however, to be more satisfactory to ul 



KU^iii 



The Characteristic Curve. 401 

Ac horse power scale at the top of the diagram, together with the 
efficiency lines already drawn, for the calculation and platting of 
the horse power curves. The horse power at any point will, of 
course, equal the theoretical horse power expressed at the upper 
margin, multiplied by the efficiency at the given points. 

In determining the horse power curve, it is best to assume the 
horse power of the desired curve, and then determine its location 
in regard to the theoretical Morse power from the equation. 
A. H. P = T. H. P. X Efficiency. 

For example, on Fig. 245, if it is desired to plat the curve rep- 
resenting 2 A. H. P. it may be done as follows: — The line repre- 
senting two actual horse power will intersect the 70% efficiency 
line at two paints whose abscissae are determined from the T. H. 
P. scale by the equation 

m rr T. A. H. P. 2 

T.H.P.=-nEl- = -770 =2.86 

If, therefore, the two points of intersection of the abscissa 2.86, 
as indicated on the upper T. H. P. scale, with the 70% efficiency 
line, are marked, two points will be established on the 2 A. H. P. 
line. As many of the lines of equal efficiency and equal horse 
power can be drawn on the diagram as may be desired, but if the 
lines of the drawing or diagram are too numerous, confusion will 
result rather than clearness. 

One of the most complete sets of experiments with, or tests of, 
a turbine water wheel which the writer has been able to obtain 
is the set of experiments made for the Tremont and Suffolk Mills 
at the Holyoke Testing Flume, December 3-5,1890, on a 48 inch 
Victor turbine, with cylinder gate (See "Notes on Water Power 
Equipment,*' by A. H. Hunking), which is given in full in Table 
LX.* 

From this table, and in the manner above described, a char- 
acteristic curve of this wheel has been prepared, and is shown by 
Fig. 245. In this Figure the efficiency curves are shown in black, 
the horse power curves are shown in red, and the lines showing 
the relations of discharge and <^ at various gate openings are 
shown by the dotted lines connecting the experimental points. 
191. The Consideration of the Turbine from its Characteristic 
Curve: — From this characteristic curve the action of the wheel 
under all conditions of operation within the experimental limits 
of ^ can be readily determined. The use of the characteristic 
• See Appendix — D. 



MOQSC POWER UNDEP 



[ ta I -i* 11 



04 




lo n 



19 IS 1^ I a ro ?o ei 



Fif, 24o. — *^Ch«raeti*ni4tir Cm 





D wiTM lOo PCPicciMT crriciewcr 



Idof Ta r b f ne* wi th C v 1 i n der G ate. 





404 



The Sdection o£ the Turbine* 



curve is based upon the assumption that the efficiency will rcmiffl ^| 
constant for a variable head as long as i^ remains constant, ^| 

The efficiency and horse power lines as interpolated, are sift- |H 
ject to errors of interpolation, the extent of which can be readily' ■*- 
judged from the diagram made< The conditions of the test m H^ 
approximately checked by this diagram, for any marked irregularis V 
ties in these curves must be doe to errors in testing, or to poor H 
workmanship. H 

By inspection it is possible to decide immodiately the vake fl 
of i> that must be maintained in order to maintain the maximum ■ 
efficiency at any particular condition of gate. For example: KB 
the maximum efficiency at full load is desired, 4> with this wheel ■ 
should equal about .69, If the maximum efficiency at 75 gate is 1 
desired, the value of <^ should be about .65, and for maximum ei- J 
ficiency at .50 g^te, 1^ should be reduced to about .64, ■ 

Knowing the head under which the wheel is to operate, the nec-^ 
essary number of revolutions at any head can be calculated by 
formula (i) or by multiplying the r* p, m, at one foot head by tk 
i/Fand the conditions of operation, in regard to both power and | 
efficiency at all gates, will be determined by the intersection of a J 
horizontal line through the chosen value of <^ with the efficiency -B 
and horse power lines. If, for example, it is decided that <^ shall ^ 
be .66, a horizontal line running directly through the diagram at 
<^=.66 will, by means of the various points of intersection with , 
the gate opening, efficiency and horse power lines, give all infor- 
mation desired and from it can be calculated the efficiency, speed, 
discharge and horse power of the wheel for the head under which 
it is to operate. The intersection of this .66 <fi line with the va- 
rious efficiency curves will give the relation of efficiency to dis- 
charge with one foot head. The discharge tinder the required 
head can be calculated by equation (8). 1* e, by multiplying the dis^ 
charge shown at the bottom of the diagram (one foot head) by V^- 
The efficiencies at each gate position will remain unchanged by 
this change in head since ^ is fixed at *66. If a 16 fool head be 
considered, the discharge at any point will be four times tlie dis- 
charge read from the diagram. 

The relation of horse power to discharge is also shown by the 
intersection of the <^ line with the horse power curves. The ac- 
tual horse power under any head can be determined by equation 
(11) i. e, by multiplying the horse power, as read from the dia- 





laractenstic Uurve. 



405 



^m (one foot head) by h\ The horse power at 16 foot head will 
^refore be 64 times that given by the diagram. 
If it is desired to utilize the characteristic cun^e for the consid* 
atioo of a wheel of another size but of the same series^ the power 

D * 
nd discharge must be multiplied by the ratio -^r 

All of the various types of curves showing the results of opera- 



in iii ii i ii ii i i m ii 



UI I I II I IIII II I I I IJ 



::aH::;:;;::;::::::::s»B»»»»:»:::»:s»:n:::n!;s'^i\s.vi:: 




4o6 The Selection of the Turbine: ^^^^ 

tion of the wheel as hitherto described are shown by, or ^di 
L calculated from, the characteristic curve. ^M 
^^ Fig. 246^ showing the relation of the number of revolutions touj 
^" efficiency and discharge of the wheel, is one example of such ul 
1 192, Other Characteristic Curves. — Fi^, 247 is the character^ 
L curve of a 44 inch "Improved New American" turbine showing tl| 

^K HORSE POWER UNDER ONE FOOT HEAD WH^H 100 PEftCOIT eTFIDIENCy 
^H ..^ 2.0 2.5 3,0 3.9 4.0 4.5 5,0 


















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^B 16 W 20 22 24 26 26 30 32 34 31 36 40 42 44 4S 48 

^H DI3CHARGC IK CURlC FCET PER 8ECDND O«J0eR CMC FOOT MEAD 

^H Pig, 247.— Chara<'ter1etlc Curve of a 44-Ineh "improved New Amei 
^^1 Turbine. . 


1 



The Characteristic Curve. 



407 



ion of the wheel through a considerable range of heads, 
utcr line entitled "Head at 120 r. p. m., shows the values of <f> 
I at which the wheel would have to operate to maintain 120 
n. at the indicated heads. The location of these points may 
termined in two ways: First. — By calculating the values of 









































































































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48. — Curves Constructed from Fig. 247 Showing the Power at Two 
Speeds of Six "Improved New American" Wheels. 



a given head and number of revolutions, and locating the 
•ponding point from the scale on the left of the diagram: 
d. — By dividing the number of revolutions by the square 
A the head and fixing the point by the corresponding revolu- 
under one foot head, as shown on the scale of r. p. m. at the 
of the diagram. 



4o8 



The Selection of the Turbine. 



At 14 foot head the wheel will operate at about the maximum ef- \ 
ficiency. If the head be decreased to 12\ the relative efficiencies | 
will still reniaiii fairly satisfactory, but will decrease rapidly at 
to' as shown by a horizDntal line drawn through the corresponding ^ 
point. It is also evident that at 8' the efficiency becomes very lo^v, 
and below this head the wheel would probably be unable to maio- 
tain 120 r, p, m. 

HO REE POWER UNDER QNC FQOT MCAD WTTM lOD l»ERC{3fT CFnCEfCr 
9r* 9,1 i.t 4.0 4.3 4 4 4.« 4. 1 l.U »,J 9.4 ** t.i 




I 



Fig. 249, — CliaracterlBtle Curves of & Wellman-Seaver-Morgan 51-lQdi M^ 

Cormick Wheel, 

The second line at the right shows the value of 4^ and xij at va- 
rious heads when operating at lOO revolutions per minute. At 
this speed the wheel will operate satisfactorily under heads from 
14' to as low as 7', or even less. The efficiency at 14 foot head io 
this case will be less than at 120 n p. m*, and the efficiency 0! oper* 
at ion will increase as the head diminishes to the g and 10 foot 
point, where the best efficiencies are obtained at 100 r, p. m. Be* 
low this point the efficiency of operation will gradually decrease. 
Provided the revolutions per minute are satisfactorily selected, \\ 
will be seen that the wheel will meet successfully a wide variatiofl 
in the operating conditions. 




The Characteristic Curve, 



409 



Fig. 248 IS a diagram constructed from this characteristic curve 
nd shov^rs the power of six turbines of this series but of 49" diam- 
ttr connected tandem to a horizontal shaft and operated at the 
'^arious heads and revolutions above discussed. The curves show 
ht condition both at full and at part gates. The gradual change 



HDUSC power UtlDEA 0N£ FOOT HEAD WTH 100 PERCENT EFnCEIIS:Y 
1.5 g.Q 2,5 3.0 3>S 4.0 4.S 5, 




I 



10 12 14 16 fS 20 22 24 26 2B 30 32 34 36 39 40 42 44 
0JSCHAR6E IN CUiiC FEET PER SECOND UNDER ONE FOOT HCAO 



W^ 260,~Char^cterlstlc Curves of the 99i4<Tnch Tremoiat Fourneyron WheeL 





H 410 The Selection gf the Turbine. 

H in the relative position of the 100 and the 120 r. p. m. curves, as 
H the head ehanges, should be noted. 

H Fig, 249 shows the characteristic curve of a 51" McCormick tur- 
H bine, as manufactured by Jolly Brothers for the Wellman-SeaveH 
H Morgan Company, At the right of the diagram are shown tlm 
H^ relative values of tf> and at the left the values of n for heads ironfl 

^^^^V MDnsc powcn unua oni: foot hcao otth ido fCRcmf trnaocir ^| 

^^^^H ^ t3 ft 77 2a 25 3Ct 3J 3i 3J 3* 23 IB 17 3M IB Aa 4\ *i Al ** 4^ *& ^ *t *9 * 1 


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OiaCNAUSC M4 CUBIC fECT f>£fl SUOMQ UMOPI OhC rOOTT HUO 

ff. 2S1. — Gbaracteristic Gurvea of a 4o-IiicJi "Samsoa* Wheel. (Jim^ 

Leffel ft Co.) 

8 feet, at go and loo r. p. m. This curve shows that this 
el will work satisfactorily under a wide range of conditions, 
suitable speed is chosen. 

g. 250 is the characteristic curve of the Tremont turbine tcstw 
ames B. Francis, and described in the "Lowell Hydraulic E*" 
ments," This wheel was a Fourneyron turbine of about 7^' 
e power at 13' head, 

g, 251 is the characteristic curve of a 45" Leffel turbine, wbitl 
been selected for the Morris Plant of the Economy Light m3< 
er Company, now under construction on the Des Plainfi* 
;r, about twelve miles south of Joliet, Illinois. 1% is to be op 
fd at 120 revolutions per minute and under variations in ht^ 



The Characteristic Curve. 



411 



n 16 to 8 feet- Eight units, each consisting of .eight of these 
^wheels, connected tandem, are to be installed to operate eight 1,000 
K. W. alternating generators. This diagram was prepared from 
the test sheet accompanying the bid of the James Lcffel & Com- 
panj. In the construction of the wheels for the plant, an attenipt 
w^as made to so alter them as to maintain a high efficiency for a 



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Fig. 252.— Characteristic Curves of a 45-lnch **Samsoii" WlieeL (James 

Leffel & Co.) 

greater range of gate conditions than ordinarily obtained. Fig, 
252 shows a characteristic curve of one of the new wheels as con- 
structed for this plant* The analysis was made for the purpose of 
estimating the results which would probably be secured under 
service. 

In Fig. 253 are shown the discharges, powers, and efficiencies 
of one unit of eight wheels under all heads from 8 to 16 feet at 
full and seven-eighths gate. Allowances would have to be made 
in order to take into account the difference between the operation 
of the eight ^vheels in the horizontal position connected in tandem , 
and in the position in which they were tested; but the diagram 





■ ^12 The Stileclion of the Turbine. 

H shown gives an analysis from which fairly satisfactory coodu* 
H stons can be drawn. 

1 193. Graphical Analysis as Developed by H, B. Taylor under 
H supervision ofW, M, White* — A valuable method of grapbbl 

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253.^ — Curves Showing the Efficiency and tlie Maximum and (MlBtfM 
Power and Discharge of One Unit ol 8 4&-Iiich Bamaon Wh^da ■ 

ysis is shown in Bulletin No. 2 of the I. P. Morris Company, fl 
:h is discussed the variations in power and efficiency of a turbiaff 
el capable of giving 13,500 horse power under a head of 65 feet, 
at a speed of 107 revolutions per minute. This wheel 1^ 
gncd by this Company for the McCall-Ferry Power Company, 
was to work under heads varying from 50 to 70 feet. - 



Graphical Analysis of W. A. Waters. 



413 




414 '^^^ Selection of ihtt Turbititf. ^^I^^| 

Figs, 254, 255 and 256 and the following description arc talccatB 
with slight alterations, from the above named Bulletin* ■ 

Curve No, i, Fi|^, 254, shows the power which the wheel will 1 
give for heads varying from 70 feet to zero» provided that the revo I 
luttons are allowed to vary as the square root of the head, anl is I 
based on equation (lo). I 

From Curve No. 1, Fig. 254, it will be noted that at 70 foot htui | 
the wheel will develop 15,000 horse power, and from Curve No. ^i. J 
of the same Figure, it will be noted that the best speed of t« 
wheel under the conditions of 70 foot head will be ni revolMtlonM 
per minute. It will also be noted from Cun^e No. i that, undtrH 
50 foot head, the wheel will develop 9,150 horse power, if it he ntd 
at 94 revolutions per minute. That is to say, by keeping a consta™ 
ratio between the peripheral speed of the runner and the sqmPM 
root of the head the efficiency of the wheel at varying heads is nofl 
changed for any given setting of the gate, I 

In order to properly utilize the output of the wheel, it is occevl 
sary that the speed be kept constant. In order to determine ik 
amount of power that will be lost by keeping the speed conftant 
while the head varies, the curves of Fig. 255 were platted from 
actual obser\^ations. 

Curve No. i, Fig. 25s, is the full gate readings of the 10,500 
horse power turbine* which was installed for the Shawinigan Wa- 
ter and Power Company, This wheel was designed for 10.500 
horse power when working under a head of 135 feet, and when 
running at 180 revolutions per minute. The observations wWch 
are platted on this curve were obtained by using the generator as 
a brake for the wheel, and a water rheostat was used as a meatisof 
loading the generator. The speed was then adjusted to 180 revolu- 
tions per minute at the wide open gate and an observation mzdt 
Ey varying the field of the generator, the speed of the unit was 
varied without materially affecting the power and without moving 
the gate of the wheel. Observations were made above and bebw 
the normal speed through as wide limits as the rheostat in the 
field circuit of the generator would permit. The power oaiiptit 
was determined by means of accurately calibrated electrical to- 
st rumen ts. The speed was determined by an accurately calibrat- 
ed tachometer. The curves on this sheet give the relation between 
^ and horse power. 

Rcterring back to Fig. 254, and taking the 50 foot head 1 
tionSi it should be noted that for a constant speed of 107 t^ 



dWitfHI^^I 



'Graphical Analysis of W. A, Waters. 



4»S 




^Cujve& of tp and Power of Several L P, Morria Wheals. { Repro- 
duced from Bull. Ho, 2 of I. P. Morn*. Co.) 




4i6 



The Selection of the Turbine, 



tions per minute 4> would have to increase from the normal vilutj 
of about ,68 to ,8a By referring again to Fig. 255, it will im 
noted that when was 0.8, with full gate opening, the power 
dropped from 10,650 horse power to 10,250 horse power, or al>oui 
3,3 per cent. From this fact the normal power as shown by Fig. 1 
may he corrected for the new speed of rotation and a point on 
Curiae No, 2, Fig, 254 obtained, giving the actual power whkli 
would be developed by the wheel under the 50 foot head, anri 
running at the constant speed of 107 revolutions per mimittJ 
Curve No, 2 is platted in this manner from Curve No. I. I 

As a check to Curve No, 1, Fig. 255, Curves Nos. 5* 6, 7, and Si 
have been platted, all of which were made from actual obseni-l 
tions, in the same manner as Curve No* i* All of these wheelfl 
are of the Francis inflow type, and were designed for ^=,7, txceptj 
Curv^e No, 6, which is an outward flow Fourneyron wheel, andB 
was designed for <^ — -5. Curve No. 5 is for a 6,000 horse powcrl 
wheel with gates in the draft tubes. The shape of the cunw 
shows that the gate was probably not entirely open when the olhB 
servations were made. ^ 

In Fig. 256 has been platted efficiency curves, which the df- 
signed wheel would give under varying heads, and running at 2 
constant number of revolutions. Curve No. i is an exact dupli* 
cate of the efficiency curve which was obtained on a 3,500 horse 
power wheel workini^ under 210 foot head, and making 250 revob- 
tions per minute. The wheel is of the Francis inflow type* with 1 
double runners, fitted with movable guide vanes, similar to \hostm 
which are proposed to be used in the wheels for the McCalKFcirfB 
Power Company, ■ 

It will be noted that the efficiency of the wheel reaches S2.3 p*"* 
cent, at about seven-eighths power, the efficiency dropping to 81 *« 
per cent, at fttll gate. It will be noted that the efficiency \$ nrfm 
high at part load. This was accomplished ^n the design of the wMB 
by sacrificing a higher efficiency at full load. This curve has !>ftr«B 
taken as typical of the efficiency which would be obtained by thcB 
wheel proposed for the McCall- Ferry Power Company, when wortj 
ing under a 65 foot head. The efficiency curve of the io.50ol^^| 
power wheel which \vas supplied by the I. P, Morris Compa^^H 
the Shawinigan A¥ater and Power Company (See Fig, 236), giv'*H 
higher results than the curve selected, but it was thought Jhal« 
Curve No. 1 is the he^t for a typical curve. ^^^^^^^^^^| 



Graphical Analysis of W. A. Waters. 417 

Curve No. i, Fig. 256 was platted by assuming that, at full gate, 
1,500 horse power corresponded to 13,500 horse power in the 
vhcel to be designed. The part gate points of the curve were ob- 
aincd by proportion. Curve No. 3 represents the efficiency and 
X)wer of the wheel when working under 50 foot head, and at 94 
r. p. m. 

Point X on this curve was obtained in the following manner: 
First, read on Curve No. 1, Fig. 254 the power which the wheel 
would give under the 50 foot head, and revolutions best suited. 
This is found to be 9,150 horse power. On Scale B, Fig. 256 a 
line is drawn from 9,150 horse power to zero, forming Curve No. 
10. To find what the efficiency would be at 8,000 horse power un- 
der the 50 foot head, take the point at 8,000 horse power on Scale 
B, projected horizontally until it intersects Curve No. 10, and 
11,800 horse power will be read from Scale A. From the effici- 
ency curve directly over 8,000 horse power on Scale A, the point, X. 
will be found on Curve No. 3, which gives the efficiency of the 
wheel when developing 8,000 horse power under the 50 foot head, 
and running at the revolutions best suited, namely 94. 

This wheel is to run, however, at 107 revolutions per minute, 
under all conditions of head, and it is necessary to correct Curve 
No. 3 for the drop in power and efficiency due to the increase in 
speed. 

Referring to Curve No. i. Fig. 255, it will be noted that the pow- 
er varies when the speed varies, and in the calculations of effi- 
ciency in Fig. 256, it has been assumed that the efficiency varies 
directly as the power. In other words, it has been assumed that 
the quantity of water does not vary when the revolutions are 
changed with the constant setting of the gate. This is not strict- 
tytrue but for the observations as platted o.n Curve No. i. Fig. 255 
the quantity of water would probably vary only one-half of one 
percent., increasing as the revolutions increase from 158 to 201. 

Referring to Fig. 254, and the 50 foot head, it will be noted that 
'vhen the speed is increased from the best speed of 94 revolutions 
the desired speed of 107 revolutions, the power falls 3.3 per 
ent. and the power and efficiency of the full gate point on Curve 
^o, 3, Fig. 256 can be decreased 3.3 per cent, resultinjg in the full 
^te point on Curve No. 2. 

Referring to Fig. 255, Curves Nos. i, 2, 3, and 4, it will be noted 
lat the slope of these curves between <^ = 0.7 and <^ - 0.8 is about 
le same, and, therefore, the power afnd efficiency of all the points 



4tH 



The Selection of the Turbine, 











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Fl|f. 256.— Eat i ma ted Efficiency— Power Ciirvea of ilie Proposed McC*ll-F€JTy 
Wheel, (Reproduced Uoin BuW, ISq, 2 vX I. P, Morris Co, ) 




Graphical Analysis of W. A. Waters. 419 

n Curve No. 3, Fig. 256, can be reduced by the same percentage, 
amely, 3.3 per cent. In this manner Curv^e No. 2, Fig. 256. is ob- 
lined, which gives the power and efficiency of the wheel when 
rorking under the 50 foot head, and running at the speed of 107 
evolutions per minute. In the same manner Curves Nos. 5 and 7 
re platted, Curves Nos. 4 and 6 being deduced therefrom, respec- 
ively. In the same manner Curve No. 9 is platted, and Curve No. 8 
educed therefrom. It will be noted that Curve No. 8 lies on the 
pposite side of the parent curve to that of the other curves, 
urve No. 8 crosses Curve No. 9 at 13,500 horse power on Scale 
., and beyond this point would drop below Curve No. 9. The 
Jason Curve No. 8 falls to the left of Curve No. 9, and shows 
reater efficiency at part gate for the 70 foot head, is because when 
changes from 0.7 to 0.65, Fig. 255, the partial gate Curves No«s. 2> 
. and 4, Fig. 255, show the increase in power and efficiency, 
hese points, however, cannot be very definitely determined, but 
docs show that the assumption is correct that the designed 
heel, working under the head of 70 feet, and running at 107 rev- 
utions, will show higher percentage of efficiency at part gate 
lan when running at the 65 foot head and the same powers. 
The curves on Fig. 256 show that the efficiency is not serious- 
affected by keeping the speed of the wheel constant under the 
irying conditions of head. They do show, however, that the 
)wer is seriously affected by keeping the speed of the wheel con- 
ant under the varying conditions of head. The endings of the 
irious curves show the maximum power, as read on Scale A, 
hich the wheels will give under that head. 

These curves, therefore, give the performance of the wheel when 
inning at a constant number of revolutions, and working under 
arying heads from 50 to 70 feet. The curves, of course, are not 
bsolutely correct. They show, however, fairly accurately, the 
mount of variation in efficiency and power which may be cx- 
ected from the actual conditions obtained with the proposed 
*ccl under the head for which it was designed. 



CHAPTER XVII 

THE LOAD CURVE AND LOAD FACTOR, AND THEIR 
INFLUENCE ON THE DESIGN OF THE POWTR 
PLANT 

194. Variation in Load. — All power plants arc subjected to more 
or less change in load» and this continually changing load has an 
iTTiportant bearing on the economy of the plant, and should be car^ 
fully considered in its design and construction. 

If the power output of any plant be ascertained, minute by mm- 
ute or hour by hour, either by means of recording devices or by 
reading the various forms of power indicators usually provided 
for such purposes, and a graphical record of such readings bf 
made, a curve varying in height, in proportion as the power varies 
from time to time, will result. This curve is termed the daily 
load curve. The load curve itself will vary from day to day ^ 
the various demands for power vary, hut it usually possesses cer-^ 
tain characteristic features which depend on the load tributary l< 
each plant and which vary somewhat as the seasons or other con- 
ditions cause the load to vary. 

The characteristics of the load curve, due to certain demands, 
can be quite safely predicted. A power plant in a large city, fofj 
example, will carry a comparatively small continuous night l<Da4j 
This, in dark weather and in winter, will he increased by the earl] 
risers who are obliged to go early to shop and factory* Tkse 
demands usually begin to affect the load curve about 5 A. M. and 
may cease wholly, or in part, by 7 A, M., depending on the seisoi 
and latitude. From 7 to 8 A. M. the motor load begins to be felt 
This may reach a maximum from 10 to T2, and usually decreases 
from 12 to 2 during the lunch hours. The maximum load usually 
comes in the afternoon when business reaches a maximum, and 
when the largest amount of power and also light (in the late after- 
noon) are used. The. load begins to decrease after the evenmg 
meal, as the demand for light lessens, and may again increase soP^ 
what as the theatres and halls open for evenings' amusements, Tht 
■character of the load curves, due to various loads, is best under- 
stood bv a study of the actual curves themselves. 



LfOad Curves of Light and Power Plants. 421 

195. Load Curves of Light and Power Plants. — ^The curves 
shown in Fig. 257 are from the plants of the Hartford Electric 
Light Co., of Hartford, Conn., and will illustrate variation of the 
Load curve at different seasons of the year. These curves were 
taken from an article in "The Electrical World and Engineer" of 
March 8th, 1902. This plant is a combined water and steam pow- 
er plant, and is provided with a storage battery to assist in equal- 
izing the load. These curves are described as follows: 

"On a week day in March, 1901, the maximum load was 1720 
k. w. and the total energy output was 30249 k. w. hours. The aver- 
age hourly load was then 1260 k. w. or 46 per cent, of the maximum 
load. On this same day the battery discharged at the rate of 260 
k. w. at the peak of the load. In the early morning hours of this day 
the load on the system, apart from battery charging, reached its 
minimum at 612 k. w., or only 22.5 per cent, of the maximum load. 
In June, 1901, the maximum load on a certain week day was 1390 
k. w., and the minimum 250 k. w., or 18 per cent, of the former. 
The total output on this day was 2505 k. w. hours, so that the 
average load during the 24 hours was 1046 k. w. or 75 per cent, of 
the maximum. In January, the maximum load came on between 
4 and 5 P. M., when lighting was the predominant factor, but in 
July the greatest demand came on the system in the latter part 
of the forenoon, and must have been made up in large part by re- 
quirements for electric power. By December 1901, the maximum 
load reached 2838 k. w. and the minimum 612 k. w. The approxi- 
mate capacity of all connected lamps and motors in that month 
was 8530 k. w. The maximum load for the December day of 2838 
k.w. is only 33 per cent, of the connected capacity. On this day 
the total output was 3219 k. w. hours, so that the average load 
during the 24 hours was 1342 k. w. This average is 15 per cent, of 
fte total capacity." 

Fig. 258 is a combined annual load curve for several years, and 
'Jot only shows the increase in the electrical output of this system 
for the years from 1898 to 1905, but also the annual monthly 
i^hange in load from a maximum in December or January to a 
minimum in June or July. This variation fortunately accompanied 
'imilar variation in the flow of the Farmington River on which 
fiost of the power was developed. 

Up to the middle of 1898 the entire load of this Company was 
arried by a single water power plant. The natural increase in 
emand for power necessitated the construction of a second plant 



121 



The Lfoad Curve, 

Kilowatts. 

§ I 




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i 



Load Curves of Light and Power Plants. 



423 



the same river, and up to January 1905, the two water power 
mts were able to carry most of the load, steam auxiliaries, how- 
er, being occasionally used, as indicated by the dotted line. 
Fig. 259 shows daily load curves from the Christiania Power 
ations, of Christiania, Norway. In this figure are shown the max- 
lum, the minimum, and a mean curve for the entire year. • The 



1000000 



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anooo 




Jan. JuL Jan Jul Jan. Jul. Jan. Jul. Jan. Jul. Jan. Jul. Jan Jul. Jan. Jul. 
1898 1800 1900 1901 1906 1908 1904 1006 



Steam 
Water 
Total 



Fig. 258.— Eneigy Output of Hartford Electric Light Co. 
Electrical World and Engineer. ) 



(From 



fFerence between the maximum and minimum curves is here very 
irked. This is readily ascribed to the high latitude of Christiania 
the long twilights of summer render lighting at that season 
Host unnecessary, while the very short and dark days of winter 
eate not only a high maximum but a high continual demand dur- 
g the entire day. No data as to kind of load is available. 
Fig. 260 is a power curve from the New York Edison Company. 
On August 1st, 1905, there were connected up to the system of 
e New York Edison Company an equivalent of 1,651,917 incan- 
scent lamps, 22,093 arc lamps, 2,539 ^' ^- ^^ storage batteries 



424 



The Load Curve. 



and 99i258 H. P, in motors. The lighting load forms 52.2 per cent^ 
of the connected load. 

The effect of extraordinary conditions on the load curv^e and I 
necessity of some kind of storage to provide for the same, is wd 
illustrated by Fig. 261 which shows the effect on the load cunci 



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Fig, 259.— Typicai Electric Lighting Load Curves. Christiana, Norwiy. 
Power Smtioni. 




of a lighting plant of a sudden thunderstorm. When such a st< 
occurs in the late afternoon the light load from schools, offio 
stores, etc., may be suddenly thrown on, and the result may be 
extraordinary load which the plant must meet. 

196, Factory Load Curves. — Shop and factory loads are suf 
posed to be the most uniform in character, yet they are subject W 
great variation, due to the sudden turning on or off of the itul- 
chines. Fig, 262 shows the load curve of the Pennsylvania Rail* 
road Shops at Altoona, Pennsylvania. 

The shops of the Pennsylvania Railroad are located in and arooni 
Altoona, Pennsylvania, in groups, each group being supplied by its 
own power station* No data as to the number and power tA motort 
connected up is available, but the following shows to some extent 
how the load is divided. The Machine Shop power plant embnrti 



Factory Load Curves. 



42s 



-300 k. w. generators, i Brush arc generator (power unknown), 
id a 40 H. P. Thompson-Houston arc generator for lighting shop 
id grounds. At the Car Shops 4-250 k. w. and 1-625 k. w. gen- 
•ators are used. Current is supplied to 75 arc lights in shops and 
ards. At the Junita shops 3-300 k. w. generators are used for 
)wcr purposes only. At South Altoona the generating station 



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New York Edieon Co., Load Curve, day of Max. load, Dec. 
•IncluiHiis 3900 K. W. delivered directly at 6600 Volts A. 0. 
Fig. 260.— Typical Electric Lighting Load Curve. 

ibraces 1-50 k. w., and 2-500 k. w., and 2-300 k. w. generators, 
e loads are quite variable, as would be expected in a railroad 
)p, there being some very heavy machines in intermittent opera- 
n, one planer running as high as 80 H. P., while 20 H. P. motors 
: numerous. The normal load is less than the maximum, but the 
ier is frequently reached. 

V, B and C, Fig. 263, are three typical factory lo5ad curves which 
resent types of load curves from three different electric power 
jonSy A in an Eastern, B in a Central, and C in a far Western 
e. These curves are taken from an article on "The Economics 
Electric Power" in Cassier's Magazine for March, 1894. The 
uits from these stations are exclusively motor circuits, the num- 
of motors connected being given in the following tables ; 



426 



The Load Curve. 



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Fig. 261. — Sharp Thunder Storm Peak, Dickenson St Station, Mancheitr. 

Eng. 



A 


B 




C 




Size of 

Motor 

<H. P.) 


No. in 
Use. 


Com- 
bined 
H. P. 


Size of 
Mot or 
(H. P.) 


No. in 
Use. 


Com- 
bined 
H. P. 


Size of 
Motor 
(H. P.) 


No. in 
Use. 


Com- 
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ap. 


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6 


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19 


57 


1 


15 


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10 


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14 


28 


3 


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12 


7i 


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6 


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120 


5 


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60 


6 


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5 


75 


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90 


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40 


10 


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150 


10 


6 


60 


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4 


100 


16 


9 


135 


14 


6 


84 


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30 
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60 
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1 
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Total... 


100 


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100 


7991 




60 


616J 



Factory Load Curves. 

i1i§§i§§§§§a 



427 




428 



The Load Curve* 



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Flff. 2S3.^Typlca] Factoir Load CtirvdB, (Caffller's Mammal oe,) 




Load Curve of London Hydraulic Company. 



429 



he circuits covered by the diagram B some of the motors are 
miles and more distant from the power stations. 
le deduction which may be made from a study of these curves 
at in an electrical power system where a considerable number 
otors are employed the initial dynamo plant need not be equal 
le total motor load. In the case in hand the curves show that 
generator need be but from 25 per cent, to 40 per cent, of the 



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264. — Maximum Days of Pumping. — London Hydraulic Supply. (Ca»- 
Bier's Magazine.) 



d capacity of the motors connected. In order to check off this 
lomenal condition actual meter readings were taken monthly 
1 fifty-three different shops covering a period of from four to 
months, current to these shops being sold on the meter basis, 
results showed that only 25V^ per cent, of the nominal capacity 
he motors was employed, thus practically checking the condi- 
s indicated by the diagrams of the central power stations. 
17. Load Curve of London Hydraulic Supply Company. — Fig. 
is a load curve of The London Hydraulic Supply Company, 
:h is rather exceptional in that the power is used almost en- 
y for running elevators and is therefore almost exclusively a 
38 



^L 430 


The Load Curve. ■ 


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A. A{, at p. BL ■ 

— T/picAl Railway Load Curve&j Internatioikal Ry. Co. (From £^i^| 
trical World and Engineer.) H 



Railway Load Curve. 431 

lay load. The London Hydraulic Supply Company furnishes 
/ater under a pressure of 750 pounds per square inch through a sys- 
era of mains 86 miles long. In 1894, 2915 machines were connected 
this system, of which 650 were passenger elevators, 2000 freight 
levators and cranes, 90 presses of various kinds, 95 motors, and 
to fire hydrants. Each 1000 gallons of water pumped represents 
1.738 H. P. hours, therefore, the maximum on the diagram repre- 
ients about 1200 H. P. The preponderant influence of the elevator 
oad is shown in the rapid rise from 6 to 10 A. M. and the some- 
what slower decline from 4 to 12 P. M. 

198. Railway Load Curves. — ^The power load most subject to 
nolent fluctations is that utilized for railway purposes. The sud- 
fcn changes in the demand for power occasioned by stopping and 
itarting of cars, which may, under some conditions, occur simul- 
taneously are often very rapid and the resulting load fluctuations 
rcry great 

Figs. 265 and 266 show two sets of curves taken from the power 
charts of the International Railway Company of Buffalo, which 
may be considered typical for electric railways. Each chart has 
two sets of curves, one for the city lines, on which the trafiic is 
purely urban in character, and the other for the Tonawanda, Lock- 
K)rt and Olcott Line, which is an interurban line. In either set the 
otal load at any time is represented by the ordinate to the highest 
urve in that set. The amount of load carried by any portion of 
le system is represented by the difference between the ordinates 
> the curve of that portion and to the curve next below. On the 
'ban lines two peaks will be observed, one at 8 A. M. and one at 
P. M., for both winter and summer, the afternoon peak of the 
rmer being nearly 75 per cent greater than the latter, however, 
he load curve of the interurban line appears to be nearly uniform 
roughout the year. 

The data, on page 432, concerning these curves are taken from 
The Electrical World and Engineer'* of December 10, 1904. 
199. Load Conditions for Maximum Returns. — It is manifest 
at no plant will receive its maximum returns without operating 

full load all of the time ; that if it operates at less than full load 
$ income will be reduced unless more is charged for power so 
jlivcred; and that if the load carried for a large portion of the 
ne is comparatively small and the returns for such power are not 
oportionately large the plant may be found to be an unprofitable 



433 



The Load Curve- 



investment. On every plant the fixed charges, which include in 
terest on first cost, depreciation charges and taxes, continue at i _ 
uniform rate every hour of the day and every day of the year* 
operating expenses increase somewhat with the total amount ofl 
power furnished but not in proportion. An increase in the total l 

Data from Curves of Figure iSS. 



Pus€HASKD Power. 



Tonawand^ 



Buffalo. 



Lock* 

port. 

nicott 



Total. 



Sto&aqe Battkbiis^' 



TonawandtL, 



Buf- 
falo. 



Lock- 
port. 



Toil] 



Told. 



Maximum H. P 
Mtnifnum H. P. 
Average H. P.. 
R P,, houna, ., 



1.667 

4,6345 

111,272 

S;J,009 



1,985 
319 

1,221 
29,302 
21,859 



8,09S 

1,985 

6,857 

140,674 

104,868 



3,752 

79 

1,262 

8,406 
6,271 



6S5 

40 

274 

3.480 
2,596 



113,' 



Maximum number of cars in sei vice in BuMalOj 406. 
Average voJte at B. C» buflbarfi, 692. 
Btata of weatber^ S a. m., cloudy; 6 p. m., fair. 
TemperatuFft; 8 a, m., 66 degreea F.; 6 p. m., 74 degrees F, 

Data from Curves of Figure JKfi* 



PuaciiAHE^o Power. 



Tofiawandot 



BtifEftlo. 



Lock* 

port, 

Oicott 



Stbim Powi 



Total* 



Niag- 
ara St 



Vir- 
ginia 
8t. 



Total. 



Buf- 
falo, 






Mflximam H. P. 

Minimum H. P. 
Avera^f* H. P... 

H. P*, hours, ..* 
K. W„ hours.,. 



7,622 

5,303 

6,002 

144,046 

107,458 



2,026 
199 

1.149 
27,584 
20,578 



9,647 

2,502 

7, 151 

171,630 

]28,03H 



3,414 
969 

2, 115 
38,442 
28,678 



2,064 

715 
1,641 
4,367 
3,238 



5.478 

l,6tt8 

3,756 

42,809 

31,93<' 



3,970 

79 

U224 

7,344 

&,47W 






Average volte at D, C. busbare, 592. 

State of weather: 8 a, m,, cloudy; 6 p. m.^ cloudy, 

Tainperature: 8 a, m., 20 degrees F.; 6 p. m. ^ degrees F» 

output of a given plant, therefore, means a direct mcrease in 1 
net earnings of the plant and unless the power plant is constifl 
operating at its maximum capacity, its earning efHciency is not 
the highest point. 




The Load Curve in Relation to Machine Selection. 433 

It will be noted at once that if a machine can be operated at its 
full capacity for the entire time, that the work done will be done 
under the most economical conditions as far as each unit of output 
(Horse Power Hour or Kilo- Watt Hour) is concerned. The in- 
terest on the first cost and other fixed charges will be distributed 
among the maximum number of power units. The cost of wear, 
and the repairs, while they increase with the amount of power fur- 
nished, are not in direct proportion thereto, and decrease per unit 
as the average load carried reaches nearer the maximum of the 
machinery used. The same is true of the cost of attendance and 
most other operating expenses. 

200. The Load Curve in Relation to Machine Selection. — A com- 
parison between the average load carried and the maximum load 
will show the relation between the machinery which it is necessary 
to install and the active work which it has to do, and furnishes a 
basis for the study of the possible earnings of the plant. 

The ratio of the average to the maximum load is called the **load 
factor." Some engineers use the term **load factor" as represent- 
ing the ratio between the average load actually carried and the 
maximum capacity of the machinery operated. The writer however, 
prefers the. term '^machine factor" to represent this ratio. The same 
term is also sometimes applied to the ratio of the average load to 
the machinery in hourly operation, but to this the term **hourly 
niachine factor" seems more applicable. The ratio of the average 
load to the total capacity of the station would seem best represented 
by the expression **capacity factor." 

In order to have a plant work at the maximum advantage, it 
niust be designed to fit the contingencies of the load. The opera- 
tion of a machine at partial load is not only expensive on the basis 
of fixed charges, but is still more so on account of the decreased 
efficiency under such conditions. 

With a varying load, efficient operation usually involves the in- 
stallation of two or more generators of such capacity that a single 
Unit will furnish the power required during the hours of minimum 
demand and at the same time operate at a fairly efficient rate. As 
the daily demand for power increases, additional units are started 
tad operated, still under economical conditions, and at the peak 
of the load one or more additional units may be cut in and operated 
For the limited time during which the maximum demands prevail. 
Such an arrangement assures reasonable economy of operation at 
all times, even when great changes of load are of daily occurrence 



434 



The Load Curve* 



aoi. Influence of Management on Load Curve* — ^The relations oi 

the "load curve," the "load factor," the "machine factor" and the 
"capacity factor" are, or may be, to an extent controlled by tbt 
business management of any plant, and by the selection and the 
character of the load to be carried, where such selection is possiye. 
Each consumer of power will develop a particular curve due to tk 
character of the work donCj and it is frequently possible, by a ju- 
dicious selection of customers, and especially by a proper gracing 
of rates, to raise the load factor and thereby decrease the cost of 
operation and increase the net profits from the plant. A study oi i 
the probable plant factors is necessary for the judicious selectio 
of machinery in order to attain the most efficient operation an(| 
in a hydraulic plant, in order to properly design it and conscr 
the maximum energy of the stream that is being developed 

202. Relation of Load Curve to Stream Flow and Auxiliaiy] 
Power. — Some of the relations between the load factor and tlifr, 
conditions under which a hydraulic plant may have to be operatc4| 
are shown by Figs. 267, 268 and 269. 

In Fig. 267, diagram A shows a typical daily load curve from tk 
terminal station at St, Louis, a curve quite similar in general char- 
acter to those previously shown. 

Diagram B shows the power that must be developed by a stream 
in order to take care of the load represented by this load cunre. 
under conditions where no auxiliary power or storage arc available. 
In this case, it will he noted that the available water power mustbej 
equivalent to or greater than the maximum peak load, and that all J 
power represented by the area above the load line, amounting in thtl 
case illustrated to about 40 per cent, of the total available pofttfjj 
will be wasted. 

Diagram C illustrates a condition where the average load aw 
water power are equal. In this case, pondage or storage, rep" 
sented by the cross-hatched area below the average Iine» may 
utilized to furnish the peak power represented by the cross-KatcWl 
area above the average line. Without pondage, the cross-hatcM 
area below the average load line will represent the energy wasted, 
and the crQss-hatched area above the average load line will Tepf^ 
sent the energy which must be supplied by auxiliary power. With- 
out pondage the power of the stream must be utilized as it parses, 
and in tlic diagram B, of Fig. 267, the power represented above th^ 
load line under such conditions must be wasted. 




Relation of Load Curve to Water Power. 



435 



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TYPICAL DAILY LOAD OURVC UNION TERMINAL ITATION IT.LOill. 







WATCI POWa ICIOilICO WITN 10 AUXILIARY POWER OR ITORAOC 




AVCRAOe LOAD AND WATER POWER EQUAL. 
ITORAOE OR A UXILIARY POWE R REQUIRED^ 






tTNAtI . 



AtllLIAfff 

Nwn. 



RELATION OF POWER SUPPLY AND DEMAND 

Fig. 267. 



43^ 



The Load Curve, 



These same conditions are shown both by diagram C, Fig* 26I 
and diagram A, Fig. 269. In the latter, with water power above 
the average load of the plant, the peak load must be supplied by 
auxiliary power, although more water power than would be suS 
cient to handle it is daily wasted. 

Diagram E, Fig. 26S, shows a condition with low water power 
no storage available, and the power less than the average load. In 
this case the water power wasted is comparatively small, and tliij 
amount, and especially the capacity, of the auxiliary power 
comes large. 

Diagram C, Fig. 268, represents a water power conditionf whert 
the power available is less than the average load, where stoi 
is practically unlimited, and some auxiliary power is necessary ii 
order to carry the peak of the load. Under these conditions, th* 
water power, which would otherwise be wasted during the \Mi 
of minimum load, is impounded, and can be utilized together witli 
the auxiliary power at times of maximum load* The diagramj 
shows a, method of utilizing the minimum capacity of auxiliai 
power by utilizing the stored water power to its greatest advii 
tage, and utilizing auxiliary power uniformly throughout th 
period where auxiliary power is demanded. 

Diagram A, Fig. 269, represqnts the same conditions where stof^ 
age is limited, and auxiliary power is necessarily required to hdj 
■out the peak load conditions. In this case only a certain amounl 
■of the spare water can be stored, the balance being wasted at tim< 
where it cannot be continuously utilized. 

The conditions for reducing the total amount of auxiliary powi 
hy utilizing the storage to advantage is shown in the same rnanm 
as in diagram C, Fig. 268* 

Diagram B, Fig. 269, shows a method of utilizing the minimui 
capacity of auxiliary power in a plant where the water power 
below the average load and the pondage is practically unlimiW 
This is accomplished by the continuous operation of the auxili! 
plant and the storage of water power during the hours of low c< 
sumption^ for utilization during the hours of peak load* 

A careful and detailed study of the load curve and load factor; 
the method of increasing the latter and of designing the most 
economical plant to take care of the condition to be met ; and the 
adjustment of rates to attain equitable returns to the investor it 
reasonable price to the consumer, are matters of plant design 
worthy of the best efforts of the engineer. 



Relation of Load Curve to Water Power. 



437 



••• 



400 



s eoo 




AUXILIARY POWeil RCQUIIIEO . NO ITillABC AVAIUIU . 
WATER POWER ORCAUR THAN AVCRAOC LOAD • 



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AOXILIARY POWCII KOIINCO . Nt tTMACE AVAILAIU •- 
WATCN nWU Ult TIAN AVCNAOC LtAO . 



400 



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100 -' 



AVCMtr LIA* 








AUXILIARY fOWER REQUIRED . OTORAOE UNLiMITED 
WATER POWER LESS THAN AVERA6E LOAD 

flTIIAtI . y'/// '■■« 






MMLIAIV 



RELATION OF POWER SUPPLY AND DEMAND . 

Fig. 268. 



433 



The Load Curve. 



SBD 



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AUXILIARY PQWtR HEqUIRCQ fiTORAOC LIMITED 
WATCR POWER GREATER THAN AVERAGE LDAO 



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m 


1 


^^H 


A,M' f.M- am* 7/1 
% II n C.4 s 1 «it i 4^ 



AUXtLIARY POWER [mIRIMUM RERUIRED] IN CONTtMtlOUa OCIVICE 
ITORAOE UNLIMITEO 



I WATCI 

j FfWtl 

I iflLIICi- 



^ 



riwii 

wAirti 



m 



lJtf»l4«E> 



fiELATtON OF PQWER SUPPLY AND OEMAHO 
Fig. 26S, 



I 




Literature on Load Curve. 439 

LITERATURE. 
REFERENCES OF LOAD CURVES AND LOAD FACTORS. 

1. Load Curves of Electric Central Station. Elektrotechnische Zeitschrift 

Vol. 25, page 68. Jan. 28, 1904. 

2. Influence of Load Factor on the Cost of Electrical Energy. Edmund L. 

Hill. Electrician (Lon.). Feb. 10, 1905. 

3. Load Factor — Its Effect upon an Electricity Station. Alex Sinclair. Else 

trician, London, June 30, 1905. 
i Distribution of Power Load of EUectricity Works. Electrician (Lon.) 
July 28, 1905. 

5. The Load Factor of EHectric Generating Stationa Norberg>^hultz. 

Cotistfania. Elektrotechnische Zeitschrift. Vol. 26, p. 919, Oct. 
6, 1905. 

6. The Effect of Load Factor on Cost of Power. E. M. Archibald. Eng. 

News, Vol. 53, p. 169. Feb. 16, 1905. Elec. Age, Nov. 1906. 

7. Electrical Transmission of Water Power. Alton D. Adams. Chap. I and 

IL New York. McGraw Pub. Co. 1906. 

8. Economy of Continued Railway and Lighting Plants. Ernest Ganzen 

bach. St. Ry. Review, Feb. 15. 1906. EHec. World and Engr 
Jan. 27, 1906. 

9. Central Station Power. E. P. Espenschied, Jr. Proc Engrs. Soc. Wes. 

Penn. Mar. 1906. 
10. Relation of Load Factor to the E^rolution of Hydro-Electric Plants. S. B. 

Storer. Am. Inst. Elec. Engrs. Mar. 23, 1906. 
U. Notes on Design of Hydro-Electric Stations (With Reference to the In 

fluence of Load Factor). David D. Rushmore. Proc. Am. Inst. 

Elec. EngTB. April, 1906. 
U. Effect of Day Load on Central Station Economy. J. P. Janes. Elec. Re 

view, N. Y. May 12, 1906. 
2. Sale and Measurement of Electric Power. S. B. Storer. EUectrical Age, 

Aug. 1906. 

4, Sale of Water Power from the Power Company's Point of View. C. E. 

Parsons. Eng. Record, Aug. 11, 1906. 

5. Contracting for Use of Hydro-Electric Power on Railway Systems. O. A. 

Harvey. Elec. Age, Sept. 1906. 
C. The Sale of Electric Power. Eng. Record, Nov. 3, 1906. 
7. Flat Rates for Small Water Power Plants. J. S. Codman. Elec Wld. 

and Engr., Nov. 3, 1906. 



CHAPTER XVIIL 

THE SPEED REGULATION OF TURBINE WATER 
WHEELS. 

203. The Relation of Resistance and Speed. — ^The power delivered 
by any water wheel may be expressed, in terms of resistance over- ' 
come by the wheel through a known distance and in a known time 
by the formula (See equation i, Section 177, Qiap. XVI). 

2jrl wn 



(1) 



P=: 



33000 



The second term of this equation may be divided into two fa^ 
tors: first, 

2irlw 

33000 
which may be called the resistance factor and which is the resist- 
ance overcome or power produced by the wheel per revolution per 




a 

? 

■0 

IS 


^^^-^^ 








> 




^^\^ 




f 






\,^ 




1 

i 

M 
•i 

a 









X^ 



aCVOUuTIONS PCR HMUTC 

Fig. 270. 

minute ; and n, the number of revolutions per minute. The product 
is the horse power of the wheel. 

In any wheel operating with a fixed gate opening and under a 
fixed head the speed, n, will always increase as the resistance, w, 
decreases, and will decrease as the resistance increases. 



Self Regulation with Variable Speed and Resistance. 441 

n Fig. 270 the line AB shows the relation of speed to resist- 
e in a turbine operated with a single fixed gate opening and 
the full range of load conditions (as determined by experiment) 
m A, at which the resistance, w, was so gp-eat as to hold the 
"tor stationary, to B where the resistance was completely re- 
'ved and the entire energy of the applied water was expended 
overcoming the friction of the wheel, or rejected as velocity en- 




Fig. 271. 



f in the water discharged therefrom. From this figure it is 
lent that if, at any fixed gate opening, a wheel is revolving at 
ven speed, n, and the resistance, w, is decreased to w" the speed 
increase to n', while if the resistance increases to w' the speed 
decrease to n'. 

34. Self-Regulation in a Plant with Variable Speed and Resist- 
t. — ^At Connorsville, Indiana, is a pumping plant (Fig. 271) in 
ch a horizontal shaft turbine is directly connected through 
tion clutches to two rotary pumps. For operation the turbine 
\s are opened until the pump, or pumps, speeding up to a suit- 
r. p. m., produces the desired pressure in the distributing sys- 



442 The Speed Regulation o£ Turbine Wate " Wheels, 

tern. The work of the pump under these conditions in pumpinf 
water at the speed of operation against the desired pressure equals 
the work done by the quantity of water q passing through the m- 
bine, less friction and other losses. If the pressure falls, the loads 
become unbalanced: i. e., the resistance is reduced and the tur- 
bine and pump increase in speed until the balance is restored. If 
the pressure rises the machine slows down until there is agsin 
a restoration of balance between the power of the turbine, the 
pump load and friction losses. 





Fig. 272. 

To pump water against an increased pressure, it is necessary to 
increase the gate opening of the turbine. In its regular daily work 
the varying demand for water is thus supplied by the self-regfula- 
tion of the two machines used and no governor is needed The 
conditions of operation are similar to those illustrated in Fig. 
270. 

205. The Kelations Necessary for Constant Speed. — Fig, 273 
is a diagram drawn from experimental or test observations afld 
similar to Fig. 270 except that the relations between speed and de- 
sistancc are shown for various gate opening. 

It IS evident that if the wheel must operate at a fixed speed, ft, 
the resistance, w, increases to v/ or decreases to w*^, it will be m 
sary to increase the gate opening from % gate to full gate in 
first case and to decrease it to % gate in the second case in order to 
maintain the speed uniform. 



k ana 
Bthe ^ 



^. The Ideal Governor. 443 

An examination of the load curves described in Chapter XVII 
shows that changes in load are constantly in progress. For the 
satisfactory operation of water wheels, under these constant and 
irregular changes in load, automatic regulation of the turbine gates 
becomes necessary* This is accomplished through the water wheel 
governor which regulates the gates through the various classes of 
gate mechanisms described in Chap. XIII. 

206. The Ideal Governor. — ^The power output of a water tur- 
bine in terms of energy applied to the wheel is expressed by the 
formula. 

(2) P = gg- where 

q s en. ft. per second of water used by the wheel. 
H' = net available head. 
E = efficiency of the wheel. 
P = hone power developed. 

Any sudden increase or decrease of load, w, will produce a cor- 
esponding decrease or increase, respectively, in the speed, n, of 
he machine as shown by Fig. 270 unless the energy applied to the 
Urbine is immediately changed to correspond. The ideal turbine 
rovernor would effect a change in output by varying only q, thus 
obtaining perfect water economy by conserving unneeded water 
or future use. This is not possible in practice as head, water, and 
herefore efficiency are usually wasted when operating a wheel un- 
i«r other than its normal load and dttring the change in load. 

207. Present Status. — ^The success of the comparatively recent 
pplication of hydraulic power to the operation of alternators in 
►arallel and to the generation of current for electric lighting street 
ailway and synchronous motor loads has been largely dependent 
ipon the possibility of obtaining close speed regulation of the gen- 
rating units accompanied with good water economy and without 
indue shock upon machinery and penstocks while working under 
iictremely variable loads. 

The degree of success thus far obtained in the development 
necessitated by the above conditioais) of automatic turbine gov- 
-rnors, although achieved from the experimental standpoint almost 
Exclusively, has been remarkable. Instances a»e now by no means 
iDcommon where hydroelectric units working upon variable loads 
^rc controlled as, satisfactorily as modern steam driven units. To 
iccomplish this result the conditions must be especially favorable. 



444 The Speed Regulation of Turbine Water Wheels, 

Success in this feature of hydra-electric design is by no meani 
uniform, however, and the frequent failure to realize satisfactoryj 
results can often be ascribed to the lack of proper consideration ( 
the arrangement of the mechanical, hydraulic^ and electrical clfr 
merits of tlie plant, wheels, and generators, rather than to anyift 
herent defects in the go\*ernor itself. The power plant, the tuts^ 
bineSi the generators, and the governors are commonly designed I 
four different parties without proper correlation of study and de- 
sign. At present neither experimental data nor theoretical fomuh 
are available by^ which the hydro-electric engineer can design m^ 
plant for an assumed speed regulation, or can predetermine eIii 
speed regulation which is possible with a given installation or t 









?oiCENT or ntntnAi iionglc pcwu 



Fig. 273. 




time required for the return to normal speed, — and yet the fp 
ernor builder is commonly required by the engineer to gnaratita 
these operating results. The predetermination otf speed v^riatio 
during portions of the steam cycle and at load changes has receive 
careful study in the design of reciprocating steam engines and 1 
desirable per cent of speed regulation is freely guaranteed 
readily obtained through careful study and analysis by the desi^tf 
The same amount of study is warranted but seldom or never giva 
to the problem of speed regulation in water power work, 

2o8, Value of Unifonn Speed. — Uniform, or nearly tinifo 
speed is of great economic value in the operation of a plant but add 
to the first cost and may also result in a waste of water. The c^ 
rect solution of any given problem of speed regulation invoh^^ 
compromise between first cost, water economy and speed reg 
tion, 

A pecuniary value cannot well be placed upon good speed reg 
lation. It differs fr»m poor speed regulation chiefly in procuring i^ 
more satisfactory operation of motor driven machinery and in pr^ 
ducing a more constant incandescent light. Fluctuations in tl 
bright ness of a light are annoying, and tend to create dissatisfi 
tion among consumers. Fig. 273 shows the general way in wHdll 



The Problem. 



4i5 



lie candle power of an incandescent light varies with the impressed 
oltage.* A pressure variation of S per cent., and hence also a 
peed variation of a similar amount, is shown to produce a much 
irger variation in candle power of the light, — in this case about 
5 to 30 per cent. 
309. The Problem. — ^Where (as in Fig. 271) a turbine is operating 
nder balanced conditions and the resistance changes in magni- 
ude, the turbine does not at once assume the new speed relations 
orresponding to the change in resistance. The inertia of the mov- 
ig parts of the wheel and of the column of water in the penstock, 




Fig. 274. 



Fig. 275. 



urbine and draft tube, tends to maintain uniformity of speed, and 
he wheel gp-adually changes in speed to that corresponding to the 
lew conditions. In such cases the speed of operation is not essen- 
ial and the delay in reaching the speed corresponding to the re- 
istancc or work the turbine must perform is usually unimportant. 

When, as in Fig. 272, the wheel is designated to operate at a 
bccd speed, the uniformity of speed becomes a matter of greater 
n less importance depending on the character of the work the wheel 
3 to perform. In this case the inertia of the wheel and of all rotat- 
Dg parts of other machinery connected thereto tends to maintain 
L constant speed. On the other hand, the flow of water in penstock, 
urbine, and draft tube must be changed in quantity, (Eq. 2), 
icnce in velocity, and its inertia therefore tends to produce a change 
n head and to produce effects opposite to those desired for efficient 
egulation. 

The conditions of installation have a marked effect on the diffi- 
ailties of turbine governing. If (as in Fig. 274) the turbine is in- 
tailed in an open pit and has only a short draft tube, and the water 

•See American Electrician, Vol. XIII, No. 7. July, 1901, by F. W. Wilcox. 
27 



4^6 The Speed Regulation of Turbine Water A^heela, 



1I0WS to the gates fram every direction, the velocity of flow km 
all directions is very low. The quantity of water which moves at a 
high velocity is confined to that in the wheel and draft tube and 
the change in the velocity and momentuni, due to, a change in the 
gates, produces no serious effects. If, however, water be con- 
ducted to and Jrom the wheel throfugh a long penstock and dfaft 
tube (as illustrated by Fig. 275) the conditions become quite differ- 
ent. In this case a large amount of energy is stored in the movii 
column of water and a change in its velocity involves a change in 
its kinetic energy which may, if an attempt is made at too rapid rej 
ulation, leave the wheel deficient in energy when increased power 6 
desired, or, when the power is decreased, may prodtice such shocks 
as will seriously affect regulation or perhaps result in serious iojui 
to the penstock and wheeh 

210. Energy Required to Change the Penstock Velocity,— j 
increase or decrease of load requires an ultimate increase or ii 
crease in velocity of the water in the penstock. Work has to 
done upon the water to accelerate it and must be absorbed in ordi 
to retard it. The total available power which can be expended h 
all purposes at any instant during the acceleration is (since vH 
proportional to qH) proportional to the product of the instantan^ 
ous velocity and the supply head. This total power is thus defi-' 
nitely limited and, hence, the work required to accelerate ihi imtir 
must be obtained at the expense of the work done upon the tvheiL 

Thus, when an increase of load occurs the gate is opened by tiie 
governor, and the immediate result is a decrease in the power out- 
put of the wheel, even below its original value, and is diametriallT 
opposed to the result desired. This counter effect may last for sev- 
eral seconds, and, unless sufficient reserve energy in some form 
is available to partially supply this deficiency^ the speed of tl 
wheel may fall considerably before readjustment to normal pow< 
can take place* 

In the same way an excess of energy must be absorbed to d< 
crease the velocity at time of decreasing load* This may be 
pended upon the wheel thus increasing the speed above normal, 
it may be dissipated in one of several ways to be discussed later 

The water in the draft tube must be accelerated and retarded 1I 
each change of gate opening and its kinetic energ>^ changed at the 
expense of the power output in exactly the same manner as that in 
the penstock. For this reason it should be included in all calcub* 
tions as a part of the penstock. One additional precaution must k 




Hunting or Racing, 



447 



n : if the draft head is large a quick closure of tlie turbine gate 
may cause the water in the draft tube to run away from the wheel 
(actually creating a vacuum in the draft tube) and then return 
again causing a destructive blow against the wheeL 

211. Hunting or Racing. — ^The regulation of both steam engines 
and hydraulic turbines as now accomplished is one of degree only 
since a departure frocm normal speed is necessary before the gov- 
ernor can act. Since the immediate effect of the gate motion is op- 
posite to that intended, the speed will depart still further from the 
normal. This tends to cause the , governor to move the gate too 
far with the result that the speed will not only return to normal 
' as soon as the inertia of the water and of the rotating parts is over- 
come, but may rush far beyond normal in the opposite direction. 
, The obvious tendency is thus to cause the speed to oscillate above 
I and below normal to the almost complete destruction of speed reg* 
lalation. 

A successful governor must therefore "anticipate" the effect of 
sny gate movement. It must move the gate to, or only slightly be- 
yond, the position which will give normal speed when readjust- 
ment to uniform flow in the penstock has taken place. A governor 
-vtnth this property or quality is commonly said to be "dead-beat/' 
In Chap. XIX several expedients are shown for the automatic clin> 
ination of excessive racing. 

aia- Nomenclature. — The following symbols will be used in the 
Tnathematical discussions which follow: 

A = cropfl iectional area of penstock m eq. ft^ 

C = friction eoefflcient for flow in pipe Ifnes = -^ (1 -|- f-^ + etc.) 

D. — miximaiii rise of watar in standpipe above^the forebay wh^ti fuil 

load ( V =2 V|) ia rejected by the wheels, 
V* = drop of water id atandpipe below original friction gradient all in- 
fluoncea considered, 
D = ditto, friction in penstock neglected, 
Dt = drop of level in standpipe below fore bay* 
d ~ diameter of penMock (closed circular) in feet. 
e — 2.7182S = base of nattiral Byeteni of logarithms, 
F = cross -Be ctional area of the atandpipe in equare feet* 
f = ^'friction factor'' in penstock. 

g — acceleration due to gravity in feet per Becx>nd per eecond. 
H = total available power head in feet. 
H' ^ effective head at the wheel = H — hf for any given uniform velocity, 
Vj in the penstock. 



44^ The Speed Rt^^ulation of Turbine Water Wheels* 

h ^ InstantAneous efieci.ve liead at the wheel dtiring chftngee of v^locltf 

in the peti-tock. 
fas = he^ wbich la effective at any logtaiit In accelerating the waitr bi 

the peiietock and draft tube. 
hr — friction lo^s in penstock for normal flow with a given head aad pit 

opening. 
bf = variable head lost by friction entrance, etc., in penstock wbaniln 

veloc'ty is v* 
I = moment of inertia or fly wheel effect of revolring parte in poimdiit 

one ft. radius = ft* lbs. 

K = energy delivered to the wheel, 

^K = excess or deficient energy delivered to wheel during change of loii 

^ Ki = excess or deficient energy delivered to wheel due to excels orddSf 

iency iti quantity of water during load change. 
^Ki= ditto, — due to energy required to accelerate or retard the wiittin 

the petutock. 
^ K|-= ditto^^due to sluggishness of gate movements 

K* = kinetic energy in foot pounds of revolving parte at speed S. 
A K'i^ increment (+ or — J in K' due to load change 

2ifH 



k' 

1 
M = elope of the v- 1 curve when v = 



2.3IV 
• leii^ah of penstock in feet^ 



V. + Vi 



(equation I@), 



pft = initial horse power output from the water wheel. 

Pl — the horse power i utput frn m the water wheel corresponding tfltk] 

new load. 
Q ££ discharge of the wheel under normal effective head H' foranjPii^l 

load, 
q = instantaneous diachai^e of wheel in cubic feet per second dunnf l«<d| 

change. 
R = ratio of actual deScient or excels work done on wheel to ibtl^i 

puted* 
S ~ normal r. p. m. of the wheel and other rotating parts. 
AS ^ S — Si = temporary change in speed. 
Si ^ speed in revolutions per minute after load change, 
T* = approximate time required lor acceleration or retarding of *i^l 

from velocity v^ to vi, 
T^ = the time required for the governor to adjust the gate after %t^^. 

of load. 
t = variable time after gate movement. 
V = normal (and hence maximum possible) velocity in the penstock i 

given head and gate opening, 
T == instantaneous variable velocity in tlie penstock while i4lQi'higt0l 

new value, 
T» = velocity in penstock at the in&tant of gate change^ 
Vi = velocity in the penstock required for new lond. 



Water Hammer- 



449 



w = weight of a cubic unit oE water ia lbs. 

Y = ma?cimtim depanure of head^ b^ from normal with use of stand- 

pi pe,^Kli9 charge gf wheel aesumed conBtant at the abnormal baa J 

(see Dp and Dt)* 
y = vanaiion of water level in thestondpipe from forebay level = H — li 
d — speed rei^ulatiori or per cent variation of speed from rjormal, 

^213, Shock or Water Hammer Due to Sudden Changes in Ve- 
locity. — The acceleration or retardation of a moving body requires 
an unbalanced force. Since acceleratiom and retardation are iden- 






-4 

'V 




WJ/ ' ^j^V4v^'fVJjj^//J^/////m^ 



tical, except as to sign, the required accelerating force may in all 
cases be expressed as follows: 

Force = masi X Rcceleratioii, 

Acceleration, or the rate at which the velocity increment in- 
creases per increment of time, is expressed by the formula: 

Pdv 
(3 ) Acceleration — —^ 

The mass of water to be accelerated is 

P (4) MaB8=^ 

Figs, 276 and 2yy show the conditions existing during an in- 
crease and decrease of velocity respectively. If the draft tube were 
closed at the lower end and no water leaving, there would be a 
total force, equal to the hydraulic pressure over the arta of the 
penstock, or wAH. tending to move the water. 





450 The Speed Regulation of Turbine Water Wheels. 

If the water is flowing with a velocity v the turbine offers a re- 
sistance to flow represented by the effective head, h, at the wheel 
and the penstock offers a resisting head hr composed of friction, en- 
trance, and other losses. If the velocity remains uniform, h==ir, 
and the forces are balanced thus : 

(6) H = H' + hr 

If the opening of the turbine gate is now suddenly increased, the 
head H' at the wheel, will fall to the value, h, (shown in Fig. 276) 
which is required to force the given amount of water, Av, througli 







Fig. 277, 

the wheel. On the other hand, if the gate opening is decreased the 
pressure head must rise above H' (as shown in Fig. 277) in order 
to discharge the water through the wheel. This change h, in the 
head H' disturbs the equilibrium of forces shown by equation 
(S) making 

(6) h. = H-h-h, 

Only the head h^ is effective in accelerating or retarding the 
water and the force resulting from this head is wAh^^. Substitut- 
ing this value and those of equations (3) and (4) in equation (2) 
we obtain: 

. , A Iw dv 
wAh. = — • -gr 

1 A'^ 1 

(7) 



or 



I J 1 

h» = — • -rr- = — X (™te of velocity change) 



Permissible Rate of Gate Movement. 451 

The value of h^ given by formula (7) is a general expression for 
le change in. pressure-head due to a change of velocity or for the 
ead which must be impressed to -produce a desired change in 
elocity. When in excess of the static pressure as shown in Fig. 
77, it is commonly called "water hammer." (See Appendix — .) 

If the closure of the gates is rapid the value of h^ is large and 
le column of water is set into vibration or oscillation. If the 
artial closure of gate is sufficiently slow to allow a distribution of 
ich increment of pressure along the pipe, this oscillatory wave is 
voided and the pressure produced at ,any instant during closure 
given by equation (7) is that which is necessary to retard the 
loving column of water at the rate at which its velocity actually 
ccreases at that instant and can be reduced below any assumed 
laximum allowable value by a sufficiently slow. gate movement. 

When a penstock is long, these oscillatory waves become • a 
ource of great danger to .the turbines and also to the penstock, 
specially at bends. The extinction of a velocity of 4 feet per 
econd at a uniform rate in one second in a pipe 1,600 feet in length 
fould create a pressure-head of about 200 feet, or a total longitud- 
lal thrust on the pipe line at each bend, and upon the wheel gate, 
f 24" in diameter, of abo,ut 20 tons. 

These dangers are further augpnented by the fact that several 
/aves, if succeeding each other by an interval which is approxi- 
nately a multiple of the vibration period of the pipe, may pile up, 
o to speak, crest upon crest and cause a pressure which no possi- 
)lc strength of parts could withstand. 



Fig. 278. 



214. Permissible Rate of Gate Movement.— Gate movements 
niust be sufficiently slow to avoid oscillatory waves of dangerous 
amplitude. No general quantitative rule can be given for the re- 
quired rate oif movement. It can be more rapid the shorter the 
penstock and the smaller the velocity in the same. The danger 
is much smaller during opening than during closure of a gate and 



452 The Speed Regulation of Turbine Water Wheels, 



the rate of gate .movement could well be made much more rapitl 
in the former than in the latter case, 

The rapidity with which a gate should be opened Is limited for! 
feeder pipes with an initial flat slope as shown in Fig* 278. 

Let h' be the lowest head obtained in opening the gmte at an as- 
sumed rate and AB, the resulting hydraulic gradient. In case thd 
gate opens so rapidly as to cause the distance, a, at any point alon^ 
the pipe to exceed suction limit, the water column it* the penstock 
will separate (the portio,n of the column above A not being able 
to accelerate as rapidly as that below) and will agiiin reunite wiili 
a severe hammer blow. Failure to observe this precaution probably 
caused the destruction of the feeder pipe of the Fresno, Caiifomta, 
power plant. The rate to be used can be chosen after a determina* 
tion, by the method discussed in Appendix — , of the pressures re- 
suiting from several assumed rates of movement. The method is tt 
dious but justifiable in many cases* 

215. Regulation of Impulse Wheels. — It is impracticable, if not 
impossible, to build a pipe line strong enough and well enougii 
anchored at all points to withstand the enormous pressures and 
longitudinal thrusts which would result from rapid gate closures 
in a long closed penstock such as commonly used for impulse 
wheels, Tbe adjustment of quantity, q, for changes in load 
short duration is hence impossible in such closed penstocks and till 
expedient usually adopted is to 'Meilect*' the jet from the wheel by 
changing the direction of discharge of a pivoted nozzle. This 
quires that the '^needle valve" (See Fig^iflS") or gate maintain a )i 
sufficient to carry peak loads; hence causmg a waste of water at all 
other times. This condition is commonly improved somewhat by 
adjusting the valve about once each hour by means of a slow niotiofl 
hand wheel for the maximum peak load liable to occur during thi 
hour. 

An automatic governor has recently been invented which mty 
the needle valve or gate slowly, thus adjusting for changes of loai 
of long duration while it still retains the deflector to provide l( 
abrupt changes in the load curve. (See Fig. /\ .) 

Another device proposed for use in this connection is a by-pasi 
nozzle arranged to open as the needle valve rapidly closes, and then 
automatically close again at a rate sufficiently slow to reduce thccs- 
cess pressure to safe limits. One advantage in fa%'or of this 
rangement is that the jet would theu always strike the center 
the buckets which is found to considerablv reduce tl*eir wear 



of. 



r^« 



ar-l 




Influence Opposing Speed Regulation. 453 

in automatic relief valve of hydraulic or spring type is nearly 
ays used but serves more as an emergency valve to reduce water 
nraer pressures than as a by-pass to divert water from the wheel 
the purpose of governing? For this latter use the spring type 
valve has proven unsatisfactory. 

n some cases the water discharged from high head plants is used 
ow for irrigation and must be kept constant, thus doing away 
h the necessity of varying the velocity in the feeder pipe for a 
ying load. 
At. Raymond D, Johnson proposes for these high head plants, 

use of large air chambers or "Surge Tanks," placed near the 
eels, of a sufficient size so that the governor can control the 
idle valve directly, thus dispensing with the deflector and by- 
;s and doing away completely with the waste of water occa- 
ned by their use. He has derived formulas by which he claims to 
rurately proportion these tanks for an assumed maximum allow- 
e range of head fluctuation or surge.* 

116. Influences Opposing Speed Regulation. — ^Abrupt changes 
the demand for power of a considerable proportion of the total 
)acity of a plant, take place at times in modern power plants. 
ree causes tend to make the change in output of a wheel lag he- 
ld the change in demand placed upon it; viz.: (i) the fact that 
J governor, however sensitive, does not act until an appreciable 
ange of speed occurs, and then not instantly ; (2) the fact that 
me time is required for the readjustment of penstock velocity, 
en after the gate movement is complete; (3) the necessity of 
anging the velocity, and hence of overcoming the inertia of the 
Iter in the penstock and draft tube at each change of load. 
Each of these influences is directly opposed to speed regulation, 

will appear in the succeeding articles, since each causes the 
)wer supplied to a wheel, at time of increasing load, to fall short 
the demand, the deficiency being supplied at the expense of the 
•ecd from the kinetic energy stored in the rotating parts. The ex- 
ession for the total deficient work, i. e. foot, pounds, is: 

(8) A K = A Ki -f A Ki -h A Ki 

r which see equations 22 and 23 and Section 221. 

217, Change of Penstock Velocity.— Assuming the gate move- 

?nt to take place instantly, we will have the condition illustrated 



See "The Surge Tank In Water Power Plants," by R. D. Johnson. Trans. 
. See. M. E.. 1908. 



454 The Speed Regulation of Turbine Water Wheeb. 

in Figs. 276 or 277, for which equation 7 was derived (Sec Sec 
213). Solving equation (7) for -g^ we have: 

(9) Acceleration = -^-- = -f" X (accelerating head) = ■?- h« 

The accelerating head as shown in equation 6 is H — h — h^ 
is the general principles of hydraulics that the head lost in 
through any opening, pipe, orifice, etc., varies as the square 
velocity. 

It was shown in Section , Chapter XVI, that the quai 
flowing through a turbine varies as the square root of the h 
Remembering that the quantity is proportional to the pensi 
velocity, we have: 

(10) -g = ^ = T/S* ^^ which 

(11) h = -^r H' Now 

(12) h, = (1 + f i. + etc.)-g- • Hence, 

(13) -t-jr or 

(14) h,=^hF 

From equation (6) 

h. = H — h — h, =x H — H' -^ — hr -^ 6r 

(16) h. = H-(H'+hF)-^ 

And from equation (5) 

(16) h. = H-H-^ = H(l — ^) 

Hence from equation (9) 

U7) dt " 1 ^ V« ' 

The integration of this equation as given in Appendix — g 
the following equatiom for the curve of velocity change in the ; 
stock following a sudden change of gate opening: 

^^^^ ^"" ^Bantilogk't+1 

As shown in Appendix B this value of v approaches but i 
equals the value of V. The form of the curve for an increa 
velocity is shown in Fig. 279. 



♦ See Merrlman'B Treatise on Hydraulics, p. , equation. 



Effect of Acceleration on Water Supplied to Wheel. 455 

218. Effect of Slow Acceleration on Water Supplied to Wheel. — 
nee velocity in the penstock, discharge of wheel, and load 
e approximately proportional to each other, the ordinates of 
g. 279 may be taken to represent loads. The load demand remains 
a constant value v© from A to B, where it suddenly increases 
Vj, foillowing the line A B C D T. The supply, howiever, 
suming an instantaneous gate movement, follows the line 
B D F. Now, the total quantity of water supplied to, and hence 




Pig. 279. 



le work (not power) done by the water upon the wheel, is propor- 
onal to the area generated by an ordinate to the latter, and the 
emand upon the wheel to the area generatd by the power curve, 
he area B C D B therefore represents a deficiency of developed 
ork which must be supplied by the energy stored in the rotating 
irts. 

For practical purposes this area may be assumed equal to the 
ea L of the triangle B' C D^ where the line B' D' is tangent to 

e curve B M D at the point of mean velocity 2^^ 

The slope of the line B' D' for this mean velocity is readily ob- 

ned from equation 17. Call it M, then 

B' 0' _ VI - vo _ gH r (vq 4- vi)' 1 
T' ~ 1 L 4V2 J 



(19) 



M = 



C D' 



and 



456 The Speed Regulation of Turbine Water Wheels. 

(20) T'=.Il^ 

(21) Area B'C'D' = L JJ^lIZloK = <^'-^o)' 

This value of L is expressed in feet and represents the dcfidcncy | 
of lineal distance moved by the water column in the penstock. Tke i 
deficiency of supplied water in cu. feet is, hence, A L and the fc j 
ficiency of undeveloped work is 

(22) A K, = ALwH = 4^ (^» - ^•)' 

219. Value of Racing or Gate Over-Run. — ^At D, Fig. 279, 4e 
supply line B D F crosses the load line C D E, and the speed wWdi 
was lost from B to D begins to pick up again. 

The necessity also for an overrun of the governor is shown by 
Fig. 279. If the demand line were A B N F and the gate opened 
to the same place as before, giving the supply line B D F, the sup- 
ply of power would approach, but theoretically never equal, the 
demand and the speed would hence never pick up to normal. The 



^__ I \ , MORMAI. OATC » MCW L.OAO ^ 

. NO WMAL Ot\T£ - OCO COAO 

Fig. 280. 

«fate movement should therefore be similar to that shown in Fig. 
280 in order to give the gate the small overrun which is necessary 
to bring the speed hack to normal. 

220. Energy Required to Change the ,Penstock Velocity. — ^The 
energy involved in the change of velocity above described result^ 
in an excess or deficiency of energy delivered to the wheel (See Sec- 
tion 210). The amount of this excess or deficient energy is readily 
determinable. The kinetic energy in foot pounds stored in the 

moving column of water is K? = —^ or 

0*? 5Alv« 
K, = •;, ' = .972 Alv« 

The amount which must be diverted from the wheel or dissipated 
when the velocity changes is therefore 

(23) A K, = 0.972 Al (vi« - Vo«)* 

In this case 1 should be taken as the combined length of penstock 
and draft tube. 



The Fly- Wheel. 457 

Tfiis deficient energy must be supplied, or the excess absorbed, by 
sans of a flywheel or the installation of a stand-pipe connected 
th the penstock closely adjoining the wheel. 

aai. Effect of Sensitiveness and Rapidity of Governor. — Referring 
ain to Fig. 279, suppose the increase of load to take place at B"*" 
ring the load line AB''' C' E. After an interval from B''' to B", 
e speed has dropped an amount depending upon the sensitiveness 
the governor. The gate will then beg^n to open ; the velocity in 
e penstock accelerating meanwhile along the dotted line B"Tf. 
le lack of sensitiveness of the governor has therefore added a de- 
ient work area of B'" B" C" C", and the slug^shness of its mo- 
rn an additional area CB" B C, approximately. This deficiency 
K, can be only roughly approximated without the detailed analy- 
I given in Appendix — . 

aaa. The Fly-WhceL — A fly-wheel is valuable for the storage 
energy. Work must be done upon it to increase its speed of rota- 
Mi,and it will again give out this energy in being retarded. From 
i« laws of mechanics the number of foot pounds of kinetic energy 
ored in a body by virtue of its rotation is given by the formula : 

^,_ 2Iir'8« _ 2X8.1416' ^ c,. «, 
^ "T^ " 32.15 X60« ^^ ""^ 

(24) K' = .00017 I 8« 

Hie amount of energy which must be g^ven to or absorbed from 
• fly-wheel in order to change the speed is 

(25) A K' = 00017 1 (So« — Si« ) 

f^us a fly-wheel can store. energy only by means of a change in 
^d. By means of a sufficiently large moment of inertia the speed 
^ge of a fly-wheel, for any given energy storage, AK', can be re- 
'ed to any desirable limit. 

^e n ed of a fly-wheel effect to carry the load of a hydro-electric 
t during changes of gate, and while the water is accelerating in 

penstock at an increase of load has led to the development of a 
« of revolving field generator, whose rotor has a high moment of 
rtia and is therefore especially adapted for speed regulation usu- 
'^ making the use of a fly-wheel unnecessary. 
Varren* has simplified the expression for AK' (See equation 

substantially as follows: 
Bee "Speed Regulation of High Head Water Wheels." by H. E. Warren. 
rechnology Quarterly, Vol. XX. No. 2. 



458 The Spt^ed Regulation of Turbine Water Wheels* 



From equation (24) : 

.^„. Ki' _ .00017 I Si' 

(27) 






K/ " S," " 8,- 



PtitSi — Si = AS 

and Ki' — K/ = £\ K' 
For small differences between S* aKd S3 equation (27) bc' 
■approximately; ' ^ 

A K^ _ 28 X A S 2 X A 8 



(28) 



K' 



Hi 



B 



or 



At. g 



V 



Or the percentage change in speed is 
(•iO) <S = ^7 — 



_ »| 

92^, The Stand-Pipe. — ^Thc function of the stand-pipe is t 

iold : (i) to act as a relief valve in case of excess pressures iji 
penstock; (2) to furnish a supply of energy to take care of sui 
increases of load while the water is accelerating, and to dissipate 
■excess kinetic energy in the moving water column at time of s^id 
drop in load. For these purposes it should be of ample diametci'i 
placed as close, to the wheel as possible. 

The analytical detemiination of the effect of a given stand-p 
upon speed regulation is very difficult if not quite impossible. F 
thermore, it is not necessary, since the drop in effective head al 
increase of load may (except in the case of maximum possible toi 
be compensated for by an increase of gate opening, hence na 
taining a constant power and speed or at least a satisfactory iem 
of speed regulation. Thus the action of a stand-pipe in sto^ 
energy differs radically from that of the fly-wheel as the latter 
store or give out energy only by means of a change of spe;. 
the generating unit. 

The determination of the range of fluctuation of water level i 
assumed stand-pipe, and the time required for return to normal I 
for various changes of load on the wheels will assist greatly in 
design of the stand-pipe. 

Fig, 281 shows the condition when a stand-pipe is used. Assi 
that the wheel is operating under part load. The water nom! 
stands a height h^ below the supply leveL If the load stidcenl| 
creases, the gates open, and the water level begins to fallp tl: js 
ing an accelerating head h. = H — h — hf. Equation 9 the 1 ap 
as before, where h^ becomes (h — cv'). 




tanc 



Ipe. 



+59 



IF the governor keeps step with the change in head by increasing 
gate opening to maintain a constant power then 

q h ^ Qi hi 
q (H - y) = Avi (H — hr ) =^ Avi (H — cvi') or 
_ Ayi{H — CV|') 

J rate of water consumption by the wheel at any instant is q; 

■it at which the water i: nipplied by the penstock is Av; and 

^« I ate of rise or fall of the water surface in stand*pipe is there* 



.31) 



q = 



(J3) 



dy _ _dh^ _ Ay — q - ^ f _ ^i (H — cvi') 1 
dt ~ dt ~ F ~F L^ H--y J 



Tl solutions of equations g and 32^ which are necessary for 
^eter nining the curves of variation of head and velocity, is imprac- 



"TJS?*^ 'Hi^b-wuDre -^ibmi 



T 




ttcablt , if not impossible, hence a different treatment is proposed and 
considered in Appendix. 

If q be assumed constant (s^Avi) during the adostment of pen- 
stock velocity and the friction loss, cv*, in the penstock be neg^lected, 
then equations 9 and 32 simplify and become integrable. The re- 
suiting equations, showing the variations of v and y, are true bar- 
monies or sine curves. The effect of friction and governor action is 
to produce a damped or somewhat distorted harmonic as discussed 
ID Appendix — ♦ Any change of load thus starts a series of wave like 
fluctuations of penstock velocity and stand*pipe level which con- 
tinue until this wave energ\'- has been entirely expended in friction. 




460 The Speed Regulation of Turbine Water Wheels, 



Analogous to all other wave motions these waves may pile up. fif 
tv^ro or more gate movements succeed each other by short inten-ali 
which are approximately multiples of the cycle, 2T) causing a fcir 
great flucuation in head and velocity. In fact by assuming a proper 
combination and succession of circumstances no limit can bcas-j 
signed to the range of fluctuation or "surge" which may occur, 
probable combination of circumstances which will occur in an? 
plant depends largely jupon the character of the load. Overflon 
from stand-pipes due to these surges have been known to do co 
siderable damage and it is desirable to either provide for this ova 
flow either at the top or by relief valves at the bottom, or builj 
the stand-pipe high enough to prevent it and thus gain the ad 
tional advantage of conserving the water which would othcrwil 
waste. 

If the change of load is assumed to occur iftVen the water is ( 
its normal level then the analysis given in Appendix — furnishes I 
followinir formulas- 



(33) 
(34) 

(35) 

(36) 
(37) 






Y^^in-y.} 



'Fg 



n i A , / I cT \ 



The value of T from equation (33) is one-half a wave cycle i 
the time required for return to normal head after a change of loa^ 
It is obtained by neglecting both friction and the compensatini 
effect of the governor, Tliese influences increase T in very ijeafl| 
the ratio that D exceeds Y* 

Y from equation (34) is the maximum head fluctuation, or max 
mum value of y, also obtained by neglecting friction and govctnaj 
action. 

D from equation (35) is the maximum drop in standpipc lev^ 
corresponding to Y except that governor action is included. 
this value of D is added as shown in equation (36) to the ixiilil 
friction loss, cv^*, the result agrees very closely with the value < 
the maximum drop D where friction is included and is much mort 
simple than the more exact equation given in Appendix — ^. 

A reasonable assumption for determining the probable maxinni 
height to which the water will rise in the stand-pipe is thtt ft 




Predetermination of Speed Regulation. 461 

id is instantly thrown off the unit when the normal full load ve- 
rity Vf exists in the penstock. This assumption leads to equa- 
« (37)- 

The verification of these formulas and some additional ones is 
^en in Appendix — , and an example of their application in sec- 
n 23a 

124. The Air Chamber. — ^There is a practical limit to the height 
which a stand-pipe can be built. A high stand-pipe is also less 
ective due to the inertia of the water in the stand-pipe itself which 
ist be overcome at each change of load, thus introducing to a 
scr degree the same problem as in a penstock without stand-pipe, 
r some such cases the top of the tank can be closed and furnished 
:h air by a compressor. The design of air chambers has been in- 
tigated by Raymond D. Johnson.* An air chamber is less effec- 
: in equalizing the pressure than a standpipe of the same diam- 
r. 

25. Predetermination of Speed Regulation for Wheels Set in 
tn Penstocks.— The influences which oppose speed regulation 
e been partly discussed. At an increase or decrease of load there 
deficiency pr excess of developed power due to (i) the inability 
:he governor to move the gate upon the instant that the load 
nges ; (2) the necessity of accelerating or retarding the water 
he penstock and draft tube as previously discussed. If no stand- 
5 is used, reliance must be .placed upon the fly-wheel effect of 
Mne, generator and additional fly wheel, if necessary, to absorb 
rive out the excess or deficiency of input over output of the plant 
his time. 

Tie first influence opposed to speed regulation, that of slow gate 
irement, is of chief importance (a) where the plant is provided 
h large open penstocks and short draft tubes ; (b) where an am- 
stand-pipe, placed close to the wheel, and a short draft tube 
used; (c) in the regulation of an impulse wheel where no at- 
pt is made to change the velocity of water in the feeder pipe. 
[f. H. E. Warrent has analyzed this case essentially as follows: 
As long as the output from the wheel is equal to the load, the 
ed S and kinetic energy K' of the revolving parts will remain 
stant. The governor is designed to adjust the output of the 
•el to correspond with the load, but it cannot do this instanta- 



See Trans, of Am. Soc. M. B., 1908. 

See article by H. E. Warren on "Speed Regulation of High Head Water 
els/' previously referred to in Section 222 
28 



462 The Speed Regnlation of Turbine Water Wheels, 

neously. Consequently, during the time T required to makcfc 
adjustment of the control mechanism after a load change there wi 
be a production of energy by the water wheel greater or less tfai 
the load. The entire excess or deficiency will be added to or sab- 
tracted from the kinetic energy of the revolving parts, and will In- 
come manifest by a corresponding change in speed. 

Neglecting friction losses, and assuming that the power of the 
water wheel is proportional to the percentage of the governor stroke 
and that the movement of the governor after a load change is ati 
uniform rate, the excess or deficient energy which goes to or comes 
from the revolving parts after an instantaneous change of load from 
Lo to Lj is measured by the average difference between the powtr 
of the wheel and the new load during the time T^, while the gover- 
nor is moving, multiplied by T" or expressed in foot pounds: 

(38) AK' =-5^^=^XT'X550 

From equation 24 the kinetic energy of the rotating parts is: 

K' = .00017 IS^ 

From equations 24, 30 and 38 

^_ 60X(Po-P.)T^X550 

2 X .00017 IS* °' 

(39) d = 81,000,000^ (po — pi) 

226. Predetermination of Speed Regulation, Plant with Closed 
Penstock. — In this case the rotating parts must absorb or deliver 
up an amount of energy AK' (equation 29), equivalent to that given 
for AK in formula 

(8) AK = AKi+ AKf+ AKf 

where, from equation 22, 

(22) ^Ki=4^(vi-v«)« 

M being obtained from equation 

The value of A K, is obtained by equation 

(23) AK, = 0.972 Al(v/-.Vo») 

There is no simple way, as discussed in section 221, of determin- 
ing K3. It must be estimated or analyzed graphically as in Appc"* 
dix C. 

From equation 

(24) K' = .00017 I S« 



Predetermination of Speed Regulation. 463 

If R is the proportion of this theoretical energy which is given to 
he rotating parts at a decrease in load,, or which the rotating parts 
nust give out during an increase of velocity and load then 

(40) AK'=BXAK 
md we have from equation 

(30) ^^.^50XRXAK| 

50X RX AK 
"• .00017 I S» °' 

(41) ^ = 294,000 5^A5 

Solving for I we find the moment of inertia of the rotating parts, 
rhich is necessary to obtain any desired percentage of regulation to 
e 

(42) 1 = 294,000 ^^s^^ 

Although there can be no doubt as to the accuracy of the form of 
[uations 41 and 42 yet their value for other than comparative pur- 
)ses depends upon the accuracy with which we can estimate R. 
'ith perfect efficiency of the wheel under all conditions, R would 
unity, but in actual cases R must be determined by experiment or 
' the graphical method given in Appendix — . It will be less for 
creasing than for increasing loads since the indficient operation 
the wheel assists speed regulation in the former case, and hinders 
in the latter. In addition to this fact, the excess energy at a de- 
ease of load can be partially dissipated through a relief valve, or 
by-pass, etc. For practical cases it is therefore necessary to in- 
stigate only the case of increasing load. 

A detailed analysis of a particular problem can be made, as in 
ppendix — , by which the velocity in the penstock, effective head, 
>wer of wheel, speed, etc., can be determined for each instant dur- 
g the period of adjustment. From this also the time of return to 
>rmal speed can be determined. The method is somewhat tedious. 
It justifiable nevertheless. 

227. Predetermination 'of Speed, Regulation, Plant with Stand- 
pe. — If the stand-pipe is of suitable diameter and close to the wheel 
e speed regulation will approach that obtainable in open penstock 
id as investigated by Warren in Section 225. Otherwise the prob- 
n becomes that of a plant with a closed penstock, of a length equal 
that of the draft tube, plus the penstock from stand-pipe to wheel. 



464 The Speed Regulation of Turbine Water Wheels, 

228. Application of Method, Closed Penstock.— An example of 
the analysis of a problem in speed regulation is as follows : 

Assume the 48" Victor cylinder gate turbine, whose characteristic 
curve is shown in Fig. 245, page — . Suppose it is supplied with 
water through a penstock whose diameter is 8 feet, jand whose 
length combined with that of the draft tube is 500 feet. The head 
is 50 feet which for ^=.664 gives 180 R. P. M. = S. 

Neglecting all losses of head except that in the turbine, we find 
from the characteristic curve for various loads as follows : 





Full load. 


.8 Load 


JiLoad. 

• 


XLoii 


Brake Horse Power 


1120.00 

240.00 

4.77 

.82 


900 
210 
4.18 
.764 


660.00 

145.00 

2.88 

.68 


280.00 


Quantity of water per sec. (cu. ft 

Velocitv in Penstock. V 


97.» 
1.91 


KfBciencv of wheel 


.505 







The above values will be considered as applying to the entirp 
plant since the loss in the penstock is small in this case. 

Assume the load to increase suddenly from one quarter load to 
0.8 load, while the gate at the same time opens to full load posi- 
tion. The nti|mber of foot pounds of work which must be done to 
accelerate the water from a velocity of 1.94 feet per second to 4.18 
feet per second is found from equation 23 to be 
AK, = 0.972 Al(vi«-.Vo*) 

= 0.972 X 60.3 X 600 (4.18» — 1.94«) 
= 0.972 X 60.3 X 600 X 13.73 
= 335,000 foot pounds. 

Referring to section 226, p. — , to find the amount of deficient 
work due to insufficient supply of water we have 



Vq + Vl _ 



From equation 19, section 226 
32.15X60 A 



M = 



600 

_ 82.15X60 
"" 600 
= 2.88 



= 3.06, 

3.O61 y 
4 X 4.77«J 

897 



From equation 22, 



^^ 50.3 X 62.6 X 60 ,, ,^ 

^^^ = 2 X2.88 ^^•^^■ 

= 187,000 foot pounds. 



1.94) • 



Predetermination of Speed Regulation. 465 

The total deficiency for which formulas have been derived is 
bence, 

A K = A Ki + A K« + (A K, undeterminable) 
= 335,000 + 137,000 
= 472,000 + ft Iba 

By means of the detailed graphical analysis given |in Appendix 
- this deficiency is found to be 600,000 foot pounds for gate move- 
nent in one-half second showing that the estimated value should 
lave been increased in this case by 12.7 per cent. (R = i.i 27) to 
:ompensate for neglecting the effect of slow (V^ second) gate move- 
ncnt, or K,. It must be remembered that this quantity, AK, is 
he deficiency of jtheoretical hydraulic work done upon the wheel. 
For reasons discussed in Appendix — , it will, however, be found to 
Jiffer but slightly from the deficiency of wheel output, in this case 
)86,ooo ft. pounds. 

To determine the speed regulation which can be obtained, as- 
sume a generating unit whose rotor has a fly-wheel effect, or mo- 
ment of inertia, I, of 1,000,000. lbs. at one ft. radius. The normal 
Jpeed S = 180, AK = 472,000 ft. lbs., and R (in general to be esti- 
nated, but in this case obtained iby the graphical method given in 
Vppendix — , is 1,127. Therefore from equation (43) 

A - 9Q4 ,^ 1.127 X 472,000 _ . .«^ 
* = ^'^1,000,000X180* - ^^^ 

If a fly-wheel is to be designed for a given regulation say 4 per 
cnt., then the required moment of inertia of same is, from equa- 
ion (42). 

I = 294,000^5^5 

= 294,000 ^^^, Of 

1 = 1,365,000 ft.* Ib0. 

229. Application of Mediod, Open Penstocks — ^As the penstock 
itid draft tube are shortened, the excess or deficient energy area, 
^^^Kj, obtained during the gate movement becomes an increasing 
proportion of the whole until for a large open penstock and short 
Iraft tube the developed power ceases to lag and follows practically 
'le same law of change as the gate opening. The estimation of 
*xcess or deficient energy, and consequently of speed, is then very 
simple by means of Mr. Warrens equation (39). For illustration: 
issume the same wheel as in the preceeding section, obtaininff 1 
outputs of 280 H. P.=Po at one-fourth load and 1120 H. P;=- 



^.66 The Sptfed Regulation of Turbine Water Wheels. 



full load, as in the other installation* Assume the same momtnl 
of inertia 1,000,000 and that the gate movement takes place in ^^ 
second as before. Then T''= H j S = 180. 
This gives 

0.5 



tf ^ S1.000,000^■ 



■(1120— 280) ^ UOSjl 



1»000»OOOX 180' 

This is a much closer regulation than obtained with the longpefr 
stock. 

230* Application o! Method, Plant with Stand-pipe-— Assume I 

plant virhere the wheels develop 39,000 H. R under 375 head, thereb; 
requiring about 1100 cu. ft- of water per second (assuming 83 pfl 
cent, efficiency of the wheels). Assume this water is supplier 
through four f pipes about 4800 feet long, requiring a velocity in t 
feeder pipes at full load of ahout 7.15 feet. Suppose four pipes i 
connected at the lower end to a stand-pipe 30 feet in diameter lia 
sudden load change, of about one third of the total is to be provided 
for this would require an ultimate change of velocity in the penstock 
from about 4.76 feet per sec. at two-thirds load to 7.15 feet at is 
loadf or v^ ^= 4.76, and v^ ^= 7.15. Now, 



4 X TT -j- = 154 aq. It 



F = ff 



30' 



= 707 



From equation 33 the time required for return to normal head, of | 
the half period of oscillation, is 



'4 



707 X 4B0i^ 



= 82 eecotidi 



'154 X 32.15 

This would perhaps be increased to nearly 100 seconds, due to the 
use of additional water during this period of low head, as disciissea| 
in Appendix — , but the value 82 should be used in equation 35. 

Equation 34 gives for the drop in water level in the stand-ptp** 



v=V: 



154 X 4800 



(7,16 — 4.76) 



707 X S2.15 

=^•30 X 2*39 - 13.6 feet. 



The more exact equations, 35 and 36, give for D and D^ 
D. - a X 3-5 D = -2-^ [^(7.15. - 4.76.) + ?!|^17.15-1«)H 



or 



D«— 750 D + 11, 120 = 




Governor Specifications- - - 467 

Solving this quadratic equation gives 

r>_760 — •750^" ^4 X 11,120 

D ^ or 

^ 760 — 719 ,,,-,, 
D = 2 = ^^'^ ^®** 

Db = 16.5 + fc X 4:.76» = 15.6 + .176 X 4.76» « 19.5 feel 

No attempt will be made 'to estimate the greatest drop in level 
hich might occur, due to an addition of waves. 

331. Governor Specifications. — ^The present practice of requiring 
!C governor builder to guarantee the speed regulation of a plants 
I the design of which he has had no voice, without even giving 
im the necessary information regarding the hydraulic elements 
hich are considered in this chapter is wrong. It is partly the out- 
rowth of the modern tendency to specialize, but perhaps more 
Tgely due to a lack of understanding on the part of the engineer of 
le nature of the problem, and a resulting desire to shift the respon- 
ibility for results upon some one else who is better informed upon 
le subject and thus protect results financially as well as save his 
wn reputation in case of failure. 

Governor specifications should call for a guarantee of the 

(a) Sensitiveness or per cent load change which will actuate the 
:overnor; 

(b) Power which the governor can develop, and force which it 
an exert to move the gates ; 

(c) Rapidity with which it will move the gates; 

(d) Anti-racing qualities, such as number of gate movements rc- 
luired to adjust for a given Iqad change (See figure 280), or per- 
cent, over-run of the gate, etc. 

(e) General requirements of material, strength, durability, etc. 
Beyond this point the governor designor has no control. The 

-ngincer can, however, by choosing a generator whose rotor has a 
"^igh moment of inertia (which quantity should be stated in tenders 
^or supplying the generators), by the addition of a fly-wheel, if 
"Accessary; by the construction of a stand-pipe; by means of a re- 
icf valve, and very largely, also, by the general design of the pen- 
Uocks, draft tubes, etc., greatly improve the governing qualities, 
^nd, in fact, reduce the speed variation to any desirable limit which 
the nature of load to be carried, magnitude of load changes antici- 
pated, and economy of first cost will warrant 



^68 The Speed Regulation ot Turbine Water Wheeli. 



LITERATimm 

Ttr RHINE ReOyLATIOTT. 

1» Wini&niB, Harrej D. A New Method ol Governing Water Whfteli. Stfc 
Jour, of Engng. ^^larch, 1896, 

2. Electric Governors. Eng, News, 1896, T<si 1, p. ^76- 

3. Parker, M. S. Governiag of Water Power Under Variable Loada, Tnm 

Am. Soc a K June* 1S97, 
' 4. Regulat[on of Wheels. The Chavanne Nozzle Regulator. Mining I Sci- 
entific PreBi, Oct, 30, 1897* 
5. Kntght, Samuel N. Water Wheel Regulation, Jour, of Elec. Not., ml 
$♦ Replogle, Mark A, Speed Government In Water-Power PI a tits. Jeur. ft 

Inst., VOL 145, p. 81, Feb., 1898. 
7- Regulation of Water Wheels under High Pressure. Pioneer Electric 
Power Co/b Wheels, Eng. Rec, Feb. 5, 189S. 

8, Garratt. Allan V* Elements of Deeign Favorable to Speed Reguiatioa. 

Eng. News, 1898, voL 2, pp, 51-159. 

9. Modern Practice In Water Wheel Operation. Elec World, May S, 1100. 

10. CasBel, Elmer F, Commercial Requirements of Water-Power Goveniiii& 

Eng, Mag., Sept.. 1900. 

11, Garratt, Allan V. Speed Reg-ulatlon of Water Power Plants. Ciasliri 

Magazine, May, 1901. 
12* A Water-Wheel Governor of Novel Construction. Eng. News* Xov. 13. 
1902. 

13. Thurso, J. W. Speed Regulation la Water Power Plants, Eng. NfWf^ 

1903, vol. 1, p, 27, 

14. Governing Impulse Wheel by an Induction Motor. Eng. News, 1903, ^oi 1' 

p. 24(3, 
1£. Garratt, Allan Y. Speed Regulation of Water Power Plants, Elec kg^ 
May, 1904. 

16. Goodman, John. The Governing of Impulse Water Wheels. Enp?- 

Nov. 4, 1904. 

17, Church, Irving P. The Governing of Impulse Wheels. Eng. Record. 

Feb. 25, 1905. 

15. GradenwitE* Alfred. The Bouvler Governor for Water TurhlQes. Marb 

N. Y. June, 1905. 

19, Henry, Geo. J„ Jr. The Regulation of High-Pressure Water-wheelB for , 

Power Tranamission Plants, Am. Soe. of Mech. Engrs. May l^l 
1906. 

20. Replogle, Mark A. Some Stepping Stones In the Development of t Mo( 

ern Water-Wheel Governor. Am. Soc. Mech. Engrs. May. W 

21, BuTtnger, Geo, A, Turbine Design as Modified for Close Regulitioa 

Am. Soc. of Mech. Engrs. May, 19p6, 

22. Lyndon, I^mar. A New Method of Turbine Control, Proc. Am. Init ( 

Elec. Engra. May, 1906, 




Literature. 469 

ater Wheel GoyemorB. Elec. World. June 30, 1906. 

New Water Wheel Governor. Eng. Rec. Current News Sup. July 14. 

1906. 
arren, H. E. Speed Regulation of High Head Water Wheels. Tech. 

Quar. Vol. 20, No. 2. 
hnson, R. D. Surge Tanks for Water Power Plants, Trans. Am. Soa M. 

B. 1908. 



CHAPTER XIX. 

THE WATER WHEEL GOVERNOR. 

a 3a, Typ«5 of Water Wheel Governors. — In all reaction turbinei 
md in all impulse turbines, with the exception of tangential wheels, 
the governor affects regulation, i. e, controls the output, and henq 
the speed of the wheel, by opening or closing the regulating \ 
thus varying the amount of water supplied to the whecL 
gential wheels, under high head, this method of control, for i 
reasons (See section 215), becomes difficult and in extremd 
impossible and in such cases the governor must be arranged 
feet regulation by the deflection of the jet from the bucket 
Fig. 2S2). 




Fig. 282. — Governing Iinpnlae ^beel with Automatic Needle and DeieetiD| ; 
Nozzle (after Warreii)* 



The force required to move the turbine gates is large (somctiflid 
50,000 lbs, or more) and it is therefore evident that they cannot I 
moved by the direct action of the centrifugal ball governors, 35 wtlj 
steam engines, but must be moved by a "relay/' 

The relay* as its name impHes, is a device for transmitting energ 
from a source of energy independent,*— as to quanlity^-of the ceft* 
trifugal governor balls but controlled by them in its appliettiQ'^ 




Typt:3 of Water Wheel Governors. 



47r 



may is of 'UneckaukQl type" the power required to operate 
the gates is transmitted, when needed, from the wheel by 
of shafts, gears, friction-clutches, belts and puUeys or other 
lica! devices. In mechanical governors the flyballs may 
' pawls, friction gears or other mechanical devices which will 
he relay into action, 




Fig, 2i3.^Woodward Standard Governor, 



» relay is of the hydrauHc type^it usually consists of a piston 
ted by some mechanical device to the gate rigging and moved 
ins of the hydraulic 'pressure of water taken from the pen- 
)r other source, or by oil supplied under high pressure from 
troin The pressure of the oil in the reservoir is maintained 
ipressed air supplied by power taken from the wheel itself, 
thus used in moving the piston is exhausted into a receiver 
hich it IS pumped back into the supply reservoir* The hy- 
ssi^y is commonly controlled by the ball governor through 



47^ 



The Water Wheel Gov ernon 



the medium of a ^rnall valve which by its motion either admits thel 
actuating water (or oil) directly to the cylinder or to a secondaryj 
piston controUing a larger admission valve. 

Electrical methods of actuating the relays controlled by mms^ 
of governor balls have been used to some extent but arc not ntarlVj 
so common as mechanical or hydraulic devices. 




Fig. 



2S4.— Dlagramatlc Section af Woodward Simple Mech&alcal 



233, Simple Mechanical Governors, — Fig, 283 is a view and Fi? 

284 a diagramatic section of a simple mechanical governor of tlif 
Woodward* Standard type. On the upright shaft are two frictio« 
pans (a and b). (See also Fig. 2S7). These pans are loc^c ot) tlif 
shaft, the upper one being supported in position by a groove in thf 
hub and the lower one by an adjustable step-bearing. Between 
these pans, and beveled to fit theni^ is a double-faced, friction whff' 
(c) which is keyed to the shaft* This shaft and friction wheel nio 



*Woo4ward Governor Co.^ Rock ford, III, 




Anti-Racing Mechanical Governors. 473 

msly and have a slight endwise movement. They are 
:d by lugs on the ball arm and therefore rise and fall as the 
of the balls varies with the speed. 

the speed is normal, the inner or friction wheel revolves 
itween the two outer wheels or pans which remain station- 
hen a change of speed occurs, the friction wheel is brought 
the upper or lower pan as the speed is either slow or fast, 
uses the latter to revolve and, by means of the bevel 
, turn the gates in the proper direction until the speed is 
)rmal. As the gate opens, the nut (d) travels along the 
t) which is driven through gearing by the main governor 
d as the g^ate reacts, the nut (d) coming in contact with 

• (f) throws the vertical shaft upward and the governor out 
ission. 

t3rpe of governor may be used to advantage where the 
heels operate a number of machines, connected to a main 
d where, in consequence, the friction or constant load is 
lerable percentage of the total load. In such cases the 
in load may not he a large percentage of the total load 
temporary variations in speed, which occur at times of 
of load, may not be of sufficient importance to necessitate 
nation of a quick acting governor. 

the water wheel is direct connected to a single machine, 
friction load is comparatively small, the relative change in 
I the consequent possible changes in speed, is much larger. 
:h cases the type of governor above shown will result in 
s hunting or racing (See Section 211) of the wheel during 
able changes of load, and in unsatisfactory regulation. In 
ses governors with compensating or anti-racing devices 
used for satisfactory regulation. 

kiiti-Racing Mechanical Governors. — ^The Woodward Com- 
g Governor. — Fig. 285 is a view and Fig. 286 is a dia- 
: section of a Woodward vertical mechanical governor of 
pensating type. 

: simple Woodward governor (See Figs. 283 and 284) the 
ecessary to actuate both the centrifugal governor balls and 
' is transmitted through a belt to a single pulley, P. In the 
ird compensating type of governor the relay is operated 
lilar manner by la single pulley, P, while the centrifugal 

• balls are actuated by an independent pulley, q, having an 
lent belt connected to the wheel shaft or to some other re- 



474 



The Water Wheel Governors. 



volving part connected therewith. From the driving pulley, % 
power is transmitted to the governor balls through a sliaft andj 
gearing. The shaft supporting the centrifugal governor 
is hollow, and on the ball-arms are two kigS which connect wilbl 




Fig. 2S5.— Woodward CoaipeiLaatiiig Govtirnor. 



spindle Cd which therefore rises and falls as the positions ottf*^ 
governor balls vary with the speed* 

The movement of the centrifugal governor balls causing *h| 
spindle^ f» to rise and fall changes the position of tlie tappet ann. 
g, to which it 19^ connected, and causes one or the other of the two 
tappets, tt', to engage a double-faced cam, h. This cam is contifr 
uously rotated by means of the pulley above it, driven by a belt com 
nected with the main veftical shaft of the relay. The tappets arc 



J 



Anti-Racing Mechanical Governors. 



475 



nnected to a common suspension arm. to which the vertical spin- 
5, f, IS attached. The suspension arm is hinged to the lever arm, j. 
le lever arm is connected to the shaft, K, which can be rotated 
its bearings and which is connected with a tension rod, 1, by an 
centric at the bottom. The tension rod, 1, is in turn connected by 




^ 2S6. — ^Diagramatic Section of Woodward Vertical Ck>mpen8ating Mechan- 
ical Governor, 



ever, m, with the vertical bearing, e, on which the main shaft of 
e friction cone rests. This bearing is movable around the ful- 
jm, n, and is counterbalanced by an arm and weight, u. 
When either of the tappets engages the rotating cam, the resulting 
>vement turns the rocker shaft, K, and, through its connection, 
ses or lowers the vertical bearing, e, which causes the friction 
leel, c, to engage either the upper or the lower of the friction 
ns, a and b, as in the case of the simple governor. 
Ihe compensating or anti-racing mechanism is just below the 
ating cam. It is essentially alike in all of the Woodward com- 
isating types of governors and is described in the govem6r cata- 
ue as follows : 



476 



The Water Wheel Covernor, 



**0n the lower end of the cam shaft is a friction disc, r, (Fig. 2%) 
which rests on a rawhide friction wheel on a diagonal shaft. The 
hub of the friction wheel is threaded and fits loosely cm the diago 
shaft which is normally at rest The effect of the continiiallT* 
rotating friction disc upon tlie rawhide wheel is evidently to cau^ 
it to travel along the threaded diagonal shaft to the center of the 
disc. When the governor moves to open or close the gate, tb 
diagonal shaft, which is geared to it, is turned and the friction 1 
is caused to travel along the shaft away from the center of the &k 



d 




I 



Fig. 297. — Friction Cone and Pans of Woodward Govereo^, 

and thus raise or lower the cam shaft so as to separate the cam ftm 
the tappet which is in action, before the gate has moved too far, 
thus preventing racing. As soon as the gate movement ceases tlie 
disc causes the friction wheel to return to the center of the disc 
along the threaded shaft," 

To prevent the governor from straining when the gate is follj 
open or closed, suitable cams are mounted on tiie stop shtll 
'*When the gates are completely opened, the cam engages the s 
lever and holds it down so that it cannot raise the lower tap 
sufficiently to engage the revolving cam; this does not, howeve 
interfere with the upper tappet, to prevent the closing of the gate 
should the conditions demand. The closed gate stop acts in a sin 
ilar manner on the upper tappet but docs not interfere with 
lower tappet being engaged, should the conditions demand that tl^ 
gate be opened. In addition to these stops, the governor is pt'i 
vided with a safety stop whose function is to immediately close 1 
gates should the speed governor stop through breakage of the I 
or any other cause." 



tfUU 



The Woodward Governor, 



477 



235. Details and Applications of Woodward Governors. — Fig. 2S7 
ows the constniction of the friction gearing of the Woodward 
echanical Governor. In the inner friction driving cone, corks 
? inserted in holes drilled in the rim and these are ground off true 
that they project about one-sixteenth inch. This seems to give a 
y reliable friction surface not readily affected by either water or 




|. 288. — Woodward Horizontal Compensating MecMntcal Governor at. Hy- 
dro-Electric Plant of U. S. Arsenal, Rock Island. 11 L 



I 



and it is claitned to he superior to either leather or paper for 
LIS purpose. In order to cause the friction wheel to engage 
noothly and nniselessly, a plunger attached to the shaft, just 
slow the inner friction wheel, fits rather closely into a dash-pot 
ffmed in the lower pan. 

Fig. 288 shows a horizontal compensating type of Woodward 
l?emor as installed to control the gates of the turbines in the Hy- 
lulic Powder Plant of the U. S. Arsenal at Rock Island, Illinois, 
he cables shown at the back of the cut operate the gates of the 
rbine. On the gate shafts of the latter are sheave wheels to which 
cables are attached. These sheave wheels are fitted with 




478 



The Walter Wheel Governor* 



clutches so that any gate may be disconnected from the fovemsfj 
Each gate is provided with an indicator showing its position TIM 
provides means of cofiipling properly, after being disconnccteU 
without closing the gates of the other wheels. Each governi^i 
arranged to control six turbines, belonging to two different unit! 
Two behs are provided so as to drive from either unit. The gove 




Fig- 2i^, — LoiJibarU-Ktf^iUtgHl Mechauical Go\*ernori 

nor can thus be used to control three wheels on either side or all 
six when the two units are running in multipl<\ 

236, The Lombard-Replogle Mechanical Governor* — Fig > 
shows a Lombard-Replogle mechanical governor. The princ: 
of operation of this governor are better illustrated in the diagram, 
Fig. 29(1 

In the diagram A is a spherical pulley with its shaft turned r 
and treaded as at X. B and B are revolving concave discs Innu 
with leather which are continuously revolving in opposite dircc' 
tions, C and C are lignum vitae pins flush with the leather* 
and D are compression springs for controlling the pressure betft^ccB 
the disks and tlic sphere. When the spherical pulley A is shifted 
from its central position in the line of its axisi the springs ait 

♦The Lombard-Replogle Governor Co., Akron^ Oliia I 



The Liombard-Replogal Mechanical Governor. 



479 



tightened automatically, causing increased traction as the smaller 
diameters of the sphere engage the larger diameters of the disc. 
E and E are the centrifugal governor balls so poised as fo require 
:hc weight of the pulley A to balance them at normal speed. F is a 
oose collar to allow independent revolution of the balls EE. G 
5 the point of connection between A and the gates or valve rigging 
f the wheel to be governed.". X is the compensating devise, and is 




Flf. 290. — ^Dlaffram of Lombard-Replogal Mechanical Gtoyemor. 



w the purpose of reducing and controlling racing. Z is a sta- 
aonary spindle or comnecting link between the collar F and the 
-hrcaded shaft or pulley A. Z is only stationary in reference to 
revolution, as it rises or falls with the variations of the governor 
balls. 

The spherical pulley A is normally at rest while the discs BB are 
continually revolving. A movement of the governor balls raises or 
lowers the shaft so that the spherical discs rotate the pulley. 

The greater the displacement of the shaft the more rapid the 
revolution since the circle of contact on the disc is increased. The 
•Qtation of the spherical pulley A either shortens or lengthens 
:hc distance to collar F by means of thread X. "This shortening 
rauscs A to be pulled back to the disc centers, thereby cutting the 
governor out of action" and preventing the gates from moving 
oo far or racing. 



Essential Features of an Hydraulic Governor. 481 

237. E^ssential Features of an Hydraulic Governor. — ^The essen- 
tial features of an hydraulic water wheel governor are : 

1. A tank for storing oil under air pressure. 

2. A receiver tank for the collection of oil used by the governor. 

3. A power pump driven from the water wheel shaft. 

4. A hydraulic power' cylinder for operating the gates. 

S- A sensitive contrifugal ball system for controlling a valve 
which cither admits oil directly to the power cylinder or to an inter- 
mediate relay cylinder the piston of which operates the admission 
valve to the power cylinder. 

6. An anti-racing or compensating mechanism. 

The power pump is continually using power from the wheel to 
pump the oil from the receiver back to the pressure tank thus 
gradually storing the energy which is used intermittently to oper- 
ate the gates. 

Fig. 291 illustrates the Lombard Type "N" Governor and shows 
clearly the relations of the various parts of an hydraulic governor. 

The centrifugal governor balls are connected by belt to the wheel 
shaft. These balls control a small primary or pilot valve of the 
cylinder type which admits oil from the large pressure tank under 
about 200 pounds pressure into one side of a cylinder where its pres- 
sure is exerted against one of two plungers. These plungers control 
a large valve, also of the cylinder type, which admits oil from the 
pressure tank to one or the other side of the power piston. The 
rectilinear motion of the piston is converted, by rack and pinion, into 
rcitary motion for transmission to the wheel gates. The oil used 
for operating the power pistons and the plungers of the relay is 
exhausted into the vacuum tank from which it is pumped back into 
^he pressure tank by means of the power pump shown at the left 
^hich is driven by belt from the wheel shaft. The speed variation 
'Necessary to actuate the governor depends upon the lap of the pilot 
^alve and is adjustable. 

238. Details of Lombard Hydraulic Governor.— The details of 
^he Lombard Type N Governor are best shown by the enlarged 
^'iew of the upper portion of the governor (Fig. 292) and by the sec- 
tion of the relay valve (Fig. 293). The following description of the 
Operation of this governor is taken from the Directions for Erecting 
^nd Adjusting Governors.* 

**The oil from the pressure-tank is supplied to the working cyl- 
inder 62 through the large relay-valve 106, arranged to discharge 

^'Published by The Lombard Governor Co., Ashland, Mass. 



483 



Hie Water Wheel Governor* 



or exhaust oil directly and rapidly into or from cither end of to 
cyUnden The relay-valve 106, through the hydraulic system con^ 
nected therewith, is under the simultaneous control of the rtg- 
ulatitig-valve 14 and the displacement-cylinder 107. This is 




aadl 



Fig, 292. — Upper Portion ot Lombard Type N Goveroor, 

brought about in the following manner The relay- valve A| 
(See Fig, 293) is moved hydraulically by plungers B 
C contained within cylinders D and E forming parts 
the relay- valve heads F and G, Plunger B has about om 
half the area of plunger C, consequently plunger C can OVCI 
power plunger B, if the pressure in cylinders E and D is nearl] 




The Lombard Governor. 



483 



al. The cylinder D is permanently in communication with the 
n pressure supply through the pipe H which also furnishes liq- 
to the regulating-valve 14, Therefore the teadency of plunger 
lalways to move valve A towards the relay-valve head G. Cy lin- 




ing. 293.— Section Lombard Relay Valve, 

I £ is in communication through pipes I and J with the adjusting- 
ve 14, and also through the pipes J and K with the displacement- 
iiadcr 107. The regulating valve 14 is capable, when moved 
One direction, of admitting liquid under full pressure into the pipe, 
aod, when moved in the other direction, of exhausting liquid 
%ugh the pipe L In the former case the action is to increase 
& pressure back of the piston C until it overpowers the piston B, 
ereby naoving valve A towards the relay-valve head F, simulta- 
iisly opening the upper cylinder-port to the main exhai'-'*^ * 




484 



The Water Wheel Governt 



the lower cylinder- port to the main pressure supply. Instantly tJill 
main piston of the governor and with it the displacement-plungefj 
109 are set in motion. 

''As the displacement-plunger begins to move, a space is create 
back of itj into which a portion of the liquid flowing through ih 
pipe I is diverted. As the motion of the displacement-plunger 1 
comes more rapid, a condition is reached v^hen all the liquid flomnj 
through I continues on through K into the displacement-chambcr| 
The relay-valve A then ceases to move any further. The motid 
of the main governor-piston, however, continues as long as thi 
regulating- valve 14 is open. When this valve 14 closes, the rclaf 
valve A is immediately thereafter closed, because the liquid in ih 
cylinder E instantly escapes through the pipes J and K into 1 
space beneath the moving displacement-plunger; thus the who 
governor is brought to rest, 

"When the regulating- valve 14 is moved in the opposite directioi 
by the centrifugal balls so as to allow liquid to escape through th<j 
pipe I, there results an immediate loss of liquid in the cylinder ] 
back of the plunger C j this allows the plunger B to force the relay 
valve A towards the relay- valve head G, thus opening the iowe 
cylinder port to the exhaust ^ and the upper cylinder-port to t^e 
pressure supply. The main governor-piston instantly begins tjo 
move down, carrying with it the displacement-plunger^ thus forcing 
liquid through the pipes K and I, reducing the flow outward throagli 
J, until finally the downward velocity of the displacement-plungtr 
becomes rapid enough to entirely check the outward flow through J 
Relay-valve A then remains stationary until the valve 14 has moved 
to a new position. As soon as regulating- valve 14 is closed, the liq- 
tiid which has been flowing out through T immediately flows into] 
and^ acting upon the plunger C, restores valve A to its closed posi-j 
tion, stoipping further movement of the governor. It will be se 
fthat the governor when moving has a constant tendency to do 
the relay- valve which keeps it in motion, and this relay-valve t^ 
'ht maintained open only so long as the regulating- valve 14 is a<i(^| 
ing or subtracting oil to or from the system consisting of the pip^ 
If J, K, and parts connected therewith*" 

Fig. 294 shows the Lomard Governor, Type R, the smallest of t^]* 
various governors made by that company* This is a vertical, s«lf*j 
contained oil pressure machine. The oil is stored in a tank forme' 
by the main frame. The go\*ernor is designed to exerl 2500 poufi^ 



k. 



The Lombard Governor. 



4^5 



pressure and will make an extreme stroke of eight inches in one 
second. 

239. Operating Results with Lombard Governor. — Fig. 295 is 
^ cut from a spead recorder strip taken from the Hudson River 




Fig, 294,— The Lombard Type R Governor. 

Power Transmission Companies plant and shows the regulation of 
Jhe Lombard Type B Governor regulating S. Morgan Smith tur- 

Iliincs on an electric railroad load. The cars are large and the 
change in load rapid and large. 




486 



The Water Wheel Governor. 




a 

o 
m 

n 



- P^ 



f:^ o 



£ 



'hi 



Fig. 296 shows the comparative repla- 
tion of two generators in the same plant 
(See Bulletin No. 107 Lombard Gow 
crnor Company,) The load was Quiltj 
variable on account of beaters whiclbd I 
to be driven from the same shaft as tliej 
paper making machinery. The ori^nall 
governor used, the work of which isshoviti 
in the upper cut, was replaced by a Lom- 
bard Type D Governor* The work qU 
the latter is shown in the lower tacho 
meter chart, and the improvement m i 
uniformity of operation is readily seen i 
a comparison of the two charts, 

240. The Sturgess Hydraulic Go?er-j 
nor,* — The Sturgess Type **M'* Hydratf 
lie Governor, with the omission of thr 
pump and storage tank, is shown in Fig 
297 and in section in Fig. 29S. This gov* 
emor consists of a shaft- tj^pc ccolnfugii 
governor G attached to the topof them*i- 
chine and operated by a belt and pullef 
P from the turbine shaft. The govemar 
balls BB in this machine control directly h 
means of a long vertical lever D a fiuall 
primary or pilot valve S of cylinder type 
which admits oil to a cylinder controlling 
the main admission valve S, The main 
valves, attached to the side of the cylin- 
der, admit pressure directly into the cyl- 
inder S and on either side of the piston ^ 
which, by its motion, rotates the gatf 
shaft by means of the concealed steel rack 
R and pinion N, shown in the scctioDal 
view, Fig, 298. 

The valves for the admission of oil or 
water, as the case may be, in the cylinder 
are of the poppet type which avoid '*lap*' 
and therefore increase the sensitivciv -? > 
the governor. The anti-racing mechdji 

^SturgeeB Enpneering Dept. of 
Valve Mfg, Ca, Troy, N, Y. 



J 



.Vheel Governor. 

The Walter Wheti ^ 




¥Vf 



-^297 



^StiJrg*^'^ 



,,.M Hydraulic Oovemc 



The Sturgess Hydraulic Governor, 

p r~t)B 



489 




Fig* 29R.— Section Slurgess Type M G^>vernor. 

nsts of a rod A which is attached to the cross head of the 
Svernor* At the top of this rod is a projection to which 
attached an adjustable piston rod reaching down into the open 
p dash pot F. The piston rod has a piston attached at its lower 

kitting freely into the bore of the dash pot the top of which is 




49© 



The Water Wheel Governor, 



formed into a cup which receives the excess oil. The bottom of tliej 
dash pat is closed and ts attached to a tail piece connected to tkj 
coonter weighted locker lever, C 

The piston rod and piston are hollow and near the bottom ^thel 
pistotti is a small by-pass which can be regulated by an adjusting 
screw which controls the rate of flow of the oil in the dash poL The 
lever, C, is fixed on the rocker shaft the opposite end of which car- 
ries the short arm from which a link is carried to the bottom of the 
valve lever D which is free to move. Two weights, EE, are 



It * I, TA^MOIICTIft N». lOpHt 

_Ti*t «. 1 H4 M _- 




o^iU^ 



^gf omar ta4 Oat*': 



m. 



w 



E-^;-- 



ii 



m 



UmA ™ - 


r-H- 


f- 


'~ 1 


-T----- 


"="F""B-- 




f- + 


^■- 


-i""- 


t:::::::-;^:::^ 


---pd^. 1.. 



Fig. 21>9.— Test Results wilti Sturgess Goveruor. 

hung loosely on the rocker shaft but a pin on the shaft engager wit^ 
either one or the other of the weights and raises them whenevertb 
rocker shaft moves. The function of the weights therefore is ' 
keep the rocker shaft, and consequently the bottom of the valv 
lever, in normal position. When the main piston moves, it is ok 
vious that it will tend to raise or lower the dash pot, F, throwg 
its connection to the rod I and this movement will swing the kv 
C and rocker shaft H thus deflecting the bottom of the valve Icvd 
Dsoas to compensate in the correct manner. The same movemcntj 
raises one of the weights E, but as the dash pot permits a iioi 
movement the weights will finally restore all parts to the middle* 



k. 



Test Results with Slurgess Cxovcmor. 



491 



normal position. In the smaller sizes the pilot valve is omitted 
and the centrifugal governor balls actuate directly through the 
lever the main valves of the system. 

241. Test Results with Sturgess Governor* — ^The action of any 
governor in maintaining a uniform speed may be shown graphi- 
cally by attaching a recording tachometer to the turbine shaft. In 
order to fully understand and appreciate the action of the governor, 
the tachometer chart should be considered together with the load 
curve and a diagram showing the movement of the governor dur- 
ing the same period* 

Fig, 299 shows a governor test made by Mn John Sturgess on an 
1 100 K* W, unit, 'The curves were traced by a special Schafer & 
Budenberg tachometer, the readings being sufficiently magnified to 
bring out the characteristics of the governor. * * * The load 
changes and governor movements are platted below. Note that when 
the whole load was thrown off (at 1 155 ), the speed accelerated about 
S per cent, in an incredibly short time (under i sec), and the gov- 
ernor had the gate shut in 14 sees, after the load went off, • * ♦ 
It is to be noted that after the first quick result at 2:00 mins. the 
governor slowly oscillated for about another minute, but with 
gradually increasing gate opening, the speed and load being prac- 
tically constant. This was due to the water rismg in the forebay, 
and gradually subsiding in a succession of waves, the governor tak- 
ing care of these fluctuations, in effective head, in a very intelligent 
manner."* 

**The plant in which these tests were made was by no means a 
good one from the regulation standpoint, for it will be noticed that 
when the whole load was instantly thrown off the momentary rise 
of speed was about 8 per cent, although the governor shut the 
gate from full open position in the extremely quick time of 1,4 
sees. There were five wicket gates, having a total of 96 leaves, and 
a heavy counter-w^eight to be moved a considerable distance in this 
interval, ** 

342, General Consideratijon. — Mechanical governors are cheaper 
than hydraulic, biit^ assuming the same gate movement, they are 
less effective at increasing loads since the power to move the gates 
must be taken as needed from the wheel itself instead of being taken 

• See American Society M, E.» Vol. 27. No, 4, p. 8* 

•• Catalo^e of Water Wheel Go?ernorB, Sturgess Engineeringf DepartmeDt 
of tfae Ludlow Valve Co.* p. 23, 



I 
I 





493 



The Water Wheel Governor 



from a storage tank as with hydaulic gfovernors. This is t factor 
of more or less importance in accordance with the degree of regu- 
lation required. The difference is manifest principally at low loads 
when the energy taken by the governor relay from the water wheel 
is a considerable percentage of the total energy being generated ^3 
the power exerted by the relay is usually comparatively small, the 
difference in action from this cause between the two types of go^ 
ernors is often unimportant- 





Fig, 300,— Governor Conneeiion by Briw BodiL 

The hydraulic governor possesses an additional advantage in its 
ability to start a stationary wheel into action by means of iu 
stored energy. The mechanical governor depending as it does on 
the power of the wheel itself is only effective after the wheel has 
been started by other means. 

243, Control From the Switchboard.— Electrical devices caa now 
be purchased by which the normal speed of the wheels can be con- 
trolled from the switchboard in case the governor is so designed, 
that it can be adjusted while in motion^ which is true of most higli| 
class machines. It is also possible to start and stop the wheeb 
electrically from the switchboard or from a distant station. 



im^ 



B ConoectioD of Governors to Gates» 493 

■ 344. Connecton of Governors to Gates, — ^The following discussion 
mi this subject and the accompanying figures are taken with slight 
changes, from a paper by Mr, A, V, Garratt.* 

" ♦ * * The most successful methofi of connecting the cylinder 
gates of several turbines to the same governor is shown in Fig. 300* 
In this case each pair of drawrods is connected to a pair of walking 
beams which carry counterweights on their opposite ends. Each 
walking beam carries a gear sector which engages a rack on a long^ 
horizontal reciprocating member terminating at the governor- 
The racks on the reciprocating member arc **sleeved*' on it, and held 
in place by pins, which may be removed if it is desired to discon- 
nect any turbine from the governor. 

"By this method any one, or any combination of turbines, may be 
handled by the governor or any turbines by hand, at will, by means 
of a lever shown in the end projection. 

"Fig. 301 shows a good method of connecting a governor to a 
pair of horizontal wicket-gate turbines. It will be noted that the 
shaft connecting the two gear sectors on the gate stems goes di- 
rectly to the governor, and is connected to it through a pin clutch 
which may be opened, and a hand- wheel cm the governor may then 
be used to move the gates by hand- The only improvement on 
this design which can be suggested would be to eliminate the coun- 
ter-shaft between the governor pulleys and the turbine shaft by plac- 
ing the governor beyond the draught*tube quarter-turn, so that 
the governor pulleys might belt directly to the turbine shaft. The 
Kmitattons of available space prevented the location of the governor 
in this manner on the drawing which shows the design used for 
three units in a modern power plant. 

"Frequently the only possible location of the governor prevents 
anything like direct connection between it and the turbines* In 
such cases experience has shown that it is wisest to avoid the use 
of several pairs of bevel gears and long shafts, and in their place 
use a steel rope drive. This method has great flexibility, and per- 
mits of governor locations which would otherwise be impossible. 
Fig. 302 shows a design of this kind. The governor is located in 
the only available space, and yet its connection to the turbines is 
perfectly adequate. The steel rope used is small in size, made of 
very small wire, especially laid up, and its ends are fixed to the 
grooved sheaves, which are provided with internal take-ups, so 

• See "Speed Regulation of Water Power Plants,* by AJlaa T. Oajrutt Ct» 
tier's MaemzlBe, May. 1901. 
3a 



t 




494 



The Water Wheel Governor. 




Fig 301 — Governor Connection by Shaft and Sectort. 



Relief Valves. 



495 



that the rope may be kept tight as a fiddle string. This general 
method of connection is in successful use in many plants where 
the requirements for speed regulation are most exacting. 

"In the above examples the two ends which have governed the 
design are simplicity and directness. These two factors should 
never be lost sight of, and the more completely they are embodied 
in the design, the better will be the sp^eed regulation. To these two 
may be added another, and that is freedom from lost motion. These 




IT 



JlL 



Fig. 302. — Governor Connection by Cable. 

three factors are absolutely necessary if successful results are to be 
expected. The slightest motion of the governor must be trans- 
mitted in the simplest and most direct manner, and in the shortest 
possible interval of time, to the turbine gates." 

245. Relief Valves. — Relief valves are very necessary on long 
feeder pipes and penstocks to avoid excess pressures of an acci- 
dental nature as well as those produced by closing of the turbine 
gates. A g^oup of such valves installed on the end of one of the 
penstocks of the Niagara Falls Hydraulic Power and Manufactur- 
ing Co. is shown in 'Fig. 303. Relief valves should be arranged to 
open with a slight excess of the penstock pressure but should close 
very slowly in order to avoid oscillatory waves. Spring hala* 



496 



The Water Wheel Governon 



relief valves have proven objectionable for this purpose. If set 
to open at a small excess pressure they are apt not to close on ac- 
count of the impact of the discharging water against the valve. 
In order that they may close, the balancing spring must be so stroaf 
That a considerable excess is required to open the valve which does 
not therefore ser\*e the desired purpose. All types of valves are 
also hindered by the fact thaf corrosion is apt to sea! the valve so 
that a considerable excess is required to open it, 
246. Lombard Hydraulic Relief Valve, — Tlxe Lonibard Gov- 




Fig. 30.1. Relief Valve on end c\i Penst-ock. Nla^ni Fn]h HyiJ rautie Pofftr 
ManufactiiilnKCo, (Electrical World, Jao. 14, IKSaj 



emor Company have designed a valve in which they claim to bvt 
eliminated the difficulties of the spring valve. This valve is shown j 
in Fig. 304* and is described as follows : 

**The valve consists of the following parts, viz: — A valve disc c* 
c&pable of motion to or from its seat, b, rigidly connected by mean? 
of a rod, ij with the piston, f, in the cylinder, e. The whole valve ti , 
bolted to a flange upon the supply pipe, d, wherein the pressure is 
to be controlled. The area of piston, f, is somewhat greater t^^^ 
that of the valve disc, c, so that when water at the same pressure j 
is behind the piston and in front of the valve there is a positive afs^ | 
strong tendency to hold the valve closed. For the purpose of a^' 



• Lombard BuHetin Ne. 101. 



Lombard Hydraulic Relief Valve. 



497 



ng the valve disc, c, to open at proper times to relieve excess 
sure in the supply pipe, d, there is provided a regulating waste 
e, C. This valve is opened or closed by a piston, n, opposed 
very oblong and strong spiral spring, p. Piston, n, is a loose 
i its cylinder, o, so that it moves upward freely in response 




Fig. 304.— Lombard Hydraulic Relief Valve. 

le least excess in pressure upward due to the water in the cyKn- 
0, apposed to the downward pressure of the spring, p. ♦ ♦ ♦ 
piston, n, is connected by means of the stem, m, with a double- 
ed balanced valve, d, which of course, opens simultaneously 
I any upward movement of the piston. Water under existing 
sure IS admitted into the cylinder, e, through the pipe, k, and 
ttle valve, t. 



498 



The Water Wheel Governor 



k. 



**Tbe spring, p* is adjusted by means of the screw, s, and lock-niit, 
jf so that the effective normal pressure of tlie water in the chamber 
13 jtist insufficient to overcome the downward pressure of the 
spring. The valve, D, will therefore remain closed normally: con- 
sequently the main valve disc, c, will also remain closed norinaUy, 
because water Bowing in through the pipe, k, and throttle %^alvf, L 
will produce an excess closing pressure upon the piston, f. When 
thus adjusted any increase in pressure above the normal will 
immediately force the piston, n, upward, and will thereby oper 
the balanced valve, D* This instanily reheves the pressure back 
of the piston, f, which of course then gives way to the superior pres- 
sure back of the piston, f, which of course then gives way to the 
superior pressure in front of valve, c. In this manner practially 
the whole pressure in front of the valve disc, c, is available fof 
opening it, * * • Valve disc, c, will continue to open until 
the limit of its travel has been reached, or the pressure in 
the supply pipe, d, has been reduced to a point where the 
piston, n, will close the balanced valve, D. Immediately on the 
closing of balanced valve, D, water begins to accumulate behind 
the piston, f, flowing in through the throttle valve, !• This water 
gradually and surely forces the valve disc, c, to close. The speed oi 
closing is adjustable by the opening through the throttle valve, i. 
and may be made as slow as several seconds or even minutes, Tlie 
closing motion is * ♦ uniform and there is not the slightest ten* 
dency to set up vibrations in the water column, a very serious ob- 
jection to the ordinary types of spring balanced valves which open 
and close suddenly and are liable in the latter operation to set np 
water hammer effects even more dangerous than those which tky 
are designed to relieve/' 

247- Sturgess Relief Valves, — The Sturgess Engineering IV 
partment of the Ludlow Valve Manufacturing Company makes two j 
forms or relief valves, the "Automatic" and the "Mechanicai 
The Automatic Relief Valve is shown in Fig. 305 and is described j 
as follows ; 

"The essential element in the Automatic Relief Valves is a largti 
very sensitive diaphragm nf special construction* This is under 
the influence of the water pressure in the pipe-line and its move 
mcnts are communicated to a small piiOt valve controlling a hr 
draulic cylinder, which in tiirm operates the relieving valve on the 
relief valve proper. After the pressure in the pipe-line is restored I 
normal, the relief valve gradually closes automatically. 




Sturgess Relief Valve. 



499 



'The action of .this valve is almost instantaneous, and it will 
fully open on a very small rise of pressure. 

"These valves can either be made in self-contained form, or 
the sensitive parts (diaphragfm, pilot valve, and hydraulic cylin- 








Fig. 305.— Sturgess Relief Valve. 

dcr) may be mounted on a pedestal placed in the power house, 
and the relief valve proper attached to the penstock or wheel cas- 
ing, a rod or link being provided to connect the two (as in Fig. 
305). 



CHAPTER XX. 
ARRANGEMENT OF THE REACTION WHEEL 



248. General Conditions. — ^The reaction turbine may be set or ar- 
ranged for scnrice in a water povirer plant in a variety of ways, and 
tlie best way may differ more or less with each installation, Tlie 
arrangement of wheels should always be made with due regard to 
machinery to be operated, the local conditions that prevail, and es- 
pecial consideration should be given to securing the greatest 
economy in the first cost of installation, maximum efficiency and 
facility in operation, and minimum cost of operation and maiflte- 
nance. 

Impulse water wheels of the tangential type have always been 
set with their shafts horizontal » An installation with vertical shaft 
was proposed for one of the first Niagara plants but was not con* 
sidered on account of the lack of actual experience with such a 
form of installation. Impulse wheels of the Girard type have been 
used with both vertical and horizontal shafts* In general* how- 
ever, because of the high heads under which impulse wheels usually 
operate, the horizontal shaft arran^gement is readily adapted. 
When an impulse wheel is installed it must be set above the level 
of maximum tail water, if it is to be operated at all stages of water, 
The wheel arrangement is therefore dependent principally on the 
arrangement of the machinery to be operated. By far the greater 
proportion of such machinery is built with horizontal shafts and 
hence in most cases wliere machinery is not special, horizontat 
shaft arrangements are desirable. 

Reaction wheels are often used on streams where the relative 
varjation in position of the tail- water is considerable, and it is both 
desirable to utilize the full head and to have the wheel set at an ele- 
vation at least above the lowest elevation of the tail- water in order 
that they may be accessible for examination and repairs. By the 
use of the draft tube this can often be done without the sacrifitc 
of head.* Tf the wheel must be set below tail-water» gates must be 
provided for the tail-race with pumps for the removal of the watcf 
when access to the wheels is necessary. 








Necessary Submergence of Reaction Wheels. 501 

The arrangement of reaction water wheels is susceptible only of 
rencral classification, which, however, may assist in the under- 
tanding of the subject and the selectioa of the best methods to be 
dopted under any set of local conditions. Wheels may be set 
ertically or horizontally, as the conditions of operation demand, 
without materially affecting their efficiency, provided that in each 
istance the turbine case, draft tubes, etc., are suitably arranged, 
'he improper design of the setting may materially affect the effi- 
iency of operation in either case. 

249. Necessary Submergence of Reaction Wheels. — In order to 
revent the formation of a vortex or whirlpool, which will draw 
ir into the wheel and often seriously affect its power and efficiency, 

is necessary that the g^te openings of the wheel be placed from 
ne to one and one-quarter wheel diameters below the water 
urface. The head under which the wheel is to operate, however, 
reatly affects the formation of the vortex. High velocities of flow 
all facilitate their formation ; therefore greater heads will require 

greater water covering or other means for the prevention of 
ortex formation. 

As the wheel usually has a greater diameter than the height of 
he gate it can be set vertically with less danger of air inter- 
crence than when set horizontally. For this reason the vertical 
vheels are more readily adapted to low heads and have in the past 
>een more widely used for developments under low and moderate 
leads. 

With both horizontal and vertical wheels the wheel may be pro- 
jected from the formation of the vortex by a solid wooden float, or 
Tiay be partially encased or covered with an umbrella-shaped cover 
the edges of which can be brought below the level of the upper 
^tes of the turbine thus allowing the wheel to be set near the 
tiead water surface without the serious interference above men- 
tioned- In all such cases the float or cover must be so arranged as 
to admit the water to the wheel gates without undue velocity in 
^rder to prevent the loss of head. If this is done the efficiency and 
>ower of the wheel will not be affected (see Appendix — ). Arrange- 
rnents of this sort were designed by the writer, in the fall of 
1^906, for the water power plants at Kilbonrn and at Dresden 
Heights. 

250. Arrangements of Vertical Shaft* Turbines. — Figs. 306 and 
507 show twelve typical arrangements of reaction turbines. Figs. 
A. B, C and D of Fig. 306 show typical arrangements of vertical 



502 



Arrangement of the Reactiott WheeL 









vmmd^^^ 



^ ■ :n 



-^z^ 



M 




Fli. SM. 





Arrangement of Vertical Siiaft Turbine. 



503 



rficels. Diagram A li the most common arrang-ement of the re- 
auction turbine in an open penstock for low head. In this case the 
•^jvhecl is set in a chamber called the wheel pit, the ftume, or some- 
times the penstock; and is connected with the head race from which 
it should be separated by gates. The wheel pits in the smaller 
fplartts have commonly been constructed of timber; but in the larger 
plants they are usually built of a more substantial character, — 
often of iron or concrete, usually reinforced. Sometimes two or 
more wheels are set in a single pit; but in the better class of con- 
struction, a pit is supplied for each individual wheel or each unit 
ccM-nbination of wheels so that each unit can be cut off from its 
fellows, disconnected from the transmission mechanism to which 
it is attached, and examined or repaired without interference with 
the remainder of the plant. Open pits are commonly used for 
heads up to 18 or 20 feet and may be used for considerably higher 
heads under favorable conditions* 

For higher heads» the arrangement shown in diagram E, or sone 
other form similar thereto, is often found more desirable. In this 
case closed flumes of steel or reinforced concrete are used, and are 
connected with the head race by metal, wooii, or reinforced con- 
crete pipes to which the term "p^^^^^^ck" is commonly applied. 
This form of construction permits of the use of vertical wheels 
with almost any head. In Diagram E the turbine is shown as di- 
rect connected to an electrical generator of special design with ver- 
tical shaft. 

In Diagram A the shaft of the turbine is shown as directly at- 
tached to a crown gear which in turn is connected by a spur gear 
with a horizontal shaft. This horizontal shaft may be direct-con-' 
nected to a generator as shown in Fig. 325, or may be attached by 
belting, ropes, cable or other mechanical means with one or more 
machines which it is designed to operate. 

Diagrams C and D show two vertical types of settings of tnn- 
dem or multiple wheels. Such arrangements are introduced when 
it is necessary to reduce the diameter of the wheels on account of in- 
creased speed, and at the same time maintain the power of in- 
stallation by increasing the number of wheels for the purpose of 
direct connection to some machine to be operated . 

In all cases where two wheels discharge into a common draft 
tube sufficient space is necessary between the wheels to prevent 
interference and consequent loss in efficiency. The arrangement 





5^4 



Arrangement of the Reaciioa Wheel 



of wheels in this manner therefore requires a considerable amount 
of vertical space and, under low or moderate head, involves the 
construction of a %vhcel pit of considerable depth in order to se- 
cure proper submergence of the upper wheeh This arrangcmcni 
results in the lower wheel being often considerably below the tail- 
water and necessitates the use of tail gates and a pumping plant 
to remove the water in order to make the lower wheels accessible 
With this design the plant is made comparatively narrow but iht 
greater depth of construction means an additional expense in the 
foundation work. Vertical wheels of all types involve a design 
of satisfactory vertical bearings which are usually less accessible 
than in the case of horizontal bearings which can be placed at an 
elevation above the power house floor, and are consequently matt 
readily accessible. The stop bearings for single vertical whcdi 
have been long in use and are reasonably satisfactory. The su 
pension bearing, which is involved in the use of large vertical in 
stallations, is not universally satisfactory and, in fact, considerable 
difficulties have been encountered in so designing a bearing that it 
will operate without undue expense for maintenance. 

251, Arrangement of Horizontal Turbines.^ — Single horizODtal 
wheels of the common type are shown in Diagrams E and F of Fig. 
306 and in Diagrams A, B, C, and D of Fig. 307. In each case thej 
gates of the turbine must be readily accessible to the entcring| 
water without undue velocity, and the wheel pit, or penstock^ must 
be designed with this requirement in view. 

Diagrams E and F, Fig. 306, and A, Fig. 307, show horizontal 
types of wheels set in an open wheel pit or penstock. 

In Diagram E the wheel has the quarter turn set entirely in the| 
pit, and the main shaft passes throug'h a bulkhead in the wall 1 
the station with a packing gland to prevent the passage of watcfJ 
In this case the water must flow by the quarter-bend and hence,' 
in order to secure sufficiently slow velocity, the wheel pit must be 
wider or deeper than in the case shown in Diagram F of Fig. i- 
Here the gates of the turbine are placed toward the entering w:itr 
and the (low is interfered with only by the pedestal bearings wl.ic];. 
being placed in the center of the crown or cover plate of the wheel 
occupy but little space and oflFer practically no obstruction to fiow. 

Diagram A of Fig. 307 is essentially the same in arrangement 
as Diagram F in Fig. 306, except that in this case instead of a m^ 
tallic quarter-turn and draft-tube, the quarter-turn and draft-tube 
are constructed in the masonry of the power station and the hnW- 



Arrangement of Horizontal Shaft Turbine. 505 









Fig. 307. 



3o6 



Arrangement of the Reaction Wheel- 



head IS reduced to simply a packing gland through which thcshaM 
enters the power station. I 

Diagrams B, C, and D, Fig. 307, illustrate three methods of en- 
closing a turbine in a closed flume which is connected with tht 
head water by a closed penstock. I 

In Diagram B the turbine case is spiral, the water enters tan^cnlj 
to the wheel and at right angles to the shaft and is discharged! 
through a metal quarter-bend into a concrete draft-tube. I 

In Diagram C the water enters the metallic flume in which thei 
wheel is placed at right angles to the shaft, and is dischaigeU 
through a metal quarter-bend and draft-tube- I 

In Diagram D the water enters the wheel case parallel to t« 
shaft of the wheel and is discharged through a metal quarter-be™ 
^nto a concrete draft-tube. I 

Figs. E and F of Fig. 307 show methods of setting homontaT 
shaft wheels in tandem. Diagram F is for setting in an opeti 
flume or penstock. The two wheels discharge into a common 
shaft chest and use a common draft-tube. In Diagram E the wbeela 
have a common closed case or flume cotmectcd by a penstock witH 
the head waters and each discharges through an independent qtiar- 
ter-turn and an independent draft-tube into the tail- waters beneatkJ 
With the closed flume removed, this arrangement can also be usefl 
in an open penstock. These diagrams are simply typical of T»*arioiii 
possible arrangements of wheels that can be adapted with variousj 
modifications of detail to meet the local requirements of the eiJ 
gmeer for any hydraulic plant which he may be called upon todoJ 
sign. I 

252, Classification of Wheels. — The classification of the amuigM 
ment of wheels as shown in Figs, 306 and 307 may be reviewe™ 
bncfly as follows: I 

In this review reference is given to various figures in the prw 
ceding and following text in which the type of wheel described Wm 
illustrated with more or less modifications^ I 

rst* Vertical single %vheel, open wheel pit (See Diagram i.^ 
Fig, 306, also Figs. 329, 331, 333 and 334,) I 

2nd* Vertical single or tandem wheels in metal casing cofM 
nectcd by cylindrical penstock with supply, (See Diagram B, Flil 
306, also Figs. 132, 181, 3T0. 31 r.) | 

3rd. Vertical tandem wheels, — two or mare wheels in open l^Jt 
(See Diagrams C and D, Fig. 306, also Figs. 134, 138. 173, 330.) 



k 




Classification of Wheels, 



507 



Horizontal turbine, open wheel pit, quart er-bend and draft- 
tube within wheel pit, — quarter bend of metaL (See Diagram E, 
Fig. 306.) 

5th* Horizontal turbine, open wheel pit, quarter-bend, and draft- 
ttibe exterior to pit, — quarter-bend may be of metal or concrete 
construction, (See Diagram F, Fig. 306, also Diagram A, Fig. 
307 and Figs, 314, 322) 

6th* Horizontal turbine in spiral case at end of penstock, single 
or double draft-tube. (See Diagram B, Fig, 307, also Figs< 159, 
162, 338.) 

7th* HorizcHntal turbine in cylindrical or conical case at end of 
penstock. (See Diagrams C and D, Fig. 307, also Fig- 335.) 

8th, Tandem horizontal turbines in open wheel pit, single dis- 
charge through common or independent draft tubes. (See Diagram 
F, Fig. 307, also Figs, 315, 319 to 324 inclusive.) 

9th, Tandem horizontal turbine in enclosed cylindrical case with 
enrnmon penstock and common or independent draft*tubes, (See 
Diagram E, Fig 307, also Figs. 13, 140, 152, 317.) 

253- Vertical Wheels and Their Connection. — The vertical set- 
ting of single wheels is usually the cheapest in first cost, which 
fact IS an important factor that has been largely ins trn mental in 
tbe adoption of this arrangement in most of the older plants. Ver- 
tical wheels are most commonly set in open wheel pits. They may, 
however, be set in a cast iron or steel casing which is then con- 
nected to the headrace or dam by a proper penstock. Single ver- 
tical wheels can be connected to the machine they are to drive by 
various means. Belting, transmission ropes, cables, and shaftings, 
arc in common tise for such connections. The shaft is usually placed 
hnrizontally and is connected by a crown beveled gear and pinion 
to the wheel. Frequently belts, ropes, and cables are connected by 
pulleys or sheaves to a short horizontal shaft driven in the same 
manner When the power of a single vertical wheel is insufficient, 
two or more may be harnessed by gearing to a line shaft which may 
be directly connected to the machin*" or machint;s to be operated, 
or otherwise connected as convenience and conditions may require. 

254. Some Installations of Vertical Water Wheels. — Figs. 329 to 
332 inclusive, show the plans, elevations, sections, and details of 
a small plant of vertical water wheels designed by the writer for 
the Sterling Gas, Light and Power company of Steriing, Illinois. 
The details of this plant are clearly shown by the illustrations and 
will b e discussed at some length later. This plant is located on the 




So8 



Arrangement of the Reaction Wheel. 

J! 



f^l^-^rjf?^ 








Some Installations of Vertical Water Wheels. 



S09 



ng side of the Rock River (See Fig» 345) and is next to the 
lant on the Sterling Race. The head developed h about eight 
and the power of each wheel is about 115 h* p. under this head. 
:h wheel of the installation is set in an independent pit or pen- 
:k which can be closed by means of a flume gate. The wheels 
connected to a common shaft extending into the power house 
Connected with pulleys and belts to the generator. 
Tie plan of the South Bend Electric Company at Buchanan, 
iiigan, is of similar type and is shown on page 544, Fig. 334. The 
!l shaft IS here connected with ten turbines and is in turn 
rtly connected to an electric alternator. 




Fig* 309, — ^1x3 w Head French Water Power Plant 



me adaptability of the vertical shaft turbine to low head is well 

Im in Figs, 308 and 309. Fig. 308 shows three turbines manufac* 

M by The Trump Manufacturing Company of Springfield, Ohio. 

ese turbines are 61 , 56 and 44" respectively, and by suitable gear- 

, are connected with a common shaft. These wheels were in- 

ed at Bologna, Italy, and operate under a low water head of 4^ 

[under a high water head of 28^ It was necessary to set the 

lis rnnsiderably below the level of the tail water in order that 

SI 



Sio 



Arrangement of the Reaction Wheel. 



the turbines should have a sufficient submergence for ope 
Fif' 3C>9 is a similar plant installed at Laches, France, In? 
case the water is conducted to the turbines by means of a syphtinj 
supply pipe in order that the turbine might be placed high eni ■:;,''' 
above tail-water that tt be accessible at all times without the 

_^ use of a tail-gate. Air i^ 

exhausted from thecrowo 
of the syphon by mt of i 
steam ejector whciicvertiK 
plant is to be started up. 
This plant operates under 
the low head of thirty-one 
inches and is said to woA 
very satisfactorily. 

Fig, 310 shows a venici] 
shaft turbine of theVictof 
cylindrical gate type maj\- 
ufactured by The PUtt 
Iron Works, This wheel 
is set in an independent 
case with provision made 
for the attachment of a 
cylindrical penstock con* 
ducting the water fromtk 
head work to the wheel 
This figure shows a special 
design by which the spec- 
ial generator is set on col- 
umns resting directly on 
the wheel case. 

Fig. 31 1 shows the plant 
of Trenton Falls, NVw 
York, of the Utica Gas and Electric Company, The wheel is a 
Fourneyron turbine, manufactured by The L P* Morris Company, 
operating under a 266 foot head, the water being conducted to the 
wheel through a penstock the length and arrangement of which art 
shown in Fig. 353. The wheel is provided with a draft- tube and is 
regularly connected with the generator above. The moving parti 
of both machines are carried by a vertical shaft bearing, shown in cut 
355, Some Installations of Vertical Wheels in Series. — In the 
last three illustrations wheels are shown of suf^cient size and operat- 




Fir 310. 




Some Installations oE Vertical Water Wheels. 



S^i 




111.— The lYentoo Falls Plant of the Utlca Gas and Electric Co. (L P. 

Morris Co.) 




5i2 



Arrangement ot the Reaction Wheel. 



ing under sufficient head to be suitable for the independent operatt! 
of the machine attached to them. In many cases, however, eif< 
cially with low head, the arrangement shown in Fig. 308 and 
Figs. 325 to 329 inclusive, becomes necessary. In such OK 
considerable loss is entailed by the use of shafts, gearings, and belt 






Fig:. 312.— Vertical Turbine for Sew airs FftlU Plant of the Concord Elect! 

These losses are so large that it is desirable to avoid oe rt 
them If possible. For this purpose vertical wheels are somel 
placed tandem as shown in Diagrams C and D, Fig, 306. 
type ol plant is also illiisLrated by Figs, 312 and 313 whicj 
illustrative of wheels tnstaUed in the plant of the Concord El 
Company, at Concord, N. H. 



Some Instalialions of Vertical Wheels in Series. 



5U 



"ig. 3T2 shows tandem wheels for this plant as designed and 
nufactured by The AUis-Chalmers Company of Milwaukee, 
s,, and are described in further detail on page 

Fig. 313 is a view of a 
double vertical unit, designed 
and built for the Concord 
Electric Company by The S* 
Morgan Smith Company of 
York, Pa. This form of in- 
stallation has the advantage 
of a greater concentration of 
the machinery This type of 
installation, while quite com- 
mon in Europe^ is somewhat 
new in this country* and pre- 
sents several novel and desir- 
able features. 

256, Some Installations 
of Horizontal Water 
Wheels.^Most machines to 
be operated by water wheels 
are built with horizontal shaft, 
and, as a direct connection of 
wheels to the machinery to 
be operated involves a min- 
imum loss in power and con- 
sequent greater efficiency 
than with the various com- 
plicated arrangements often 
necessary with vertical 
wheels, the horizontal wheel 
becomes desirable and is 
opted whenever practicable in a modern water power plant. The 
pe of such a plant is well illustrated by the power plant at Turner's 
4is, Massachusetts^ shown by Fig. 314. The single horizontal wheel, 
*ect-connected to the machinery to be operated, is perhaps already 
Rficiently described in the preceding pages. The arrangement of 
o or more wheels for such purposes deserves careful consideration, 
gs. 315 and 316 show a plan and section of a double unit, for use in 
open penstock, as manufactured by The Dayton Globe Iron 
orks Company of Dayton, Ohio, These figures show a plain. 




Fig. S13. 





Some Installations of Horizontal Water Wheels. 515 

idrical, draft-chest connected with a common draft-tube. The 
ils of the arrangement can perhaps be better seen from the half- 
, Fig. 320. which illustrates two of these units connetcd 
ther tandem. 




^ggr>ii*r<i>tiii^'i.rt«y 



315. — Section Double Wheel with Common Draft Tube. (Dayton, Globe 
Iron Worics Co.) 




Fig. 316.— Plan. 



igs. 317 and 318 show a similar double unit manufactured by 
same company. This unit is shown set in a closed flume for 
nection by a penstock of suitable size with the head works. In 
. 318 the chest, into which the turbines dischargee, is designed 
IS to give a certain independence to the discharge of the two 
)incs until they come to the draft-chest below the wheel. The 
)ine case, shown in Fig. 316, seems to have more room than 



s^ 



Arrangement of the Reaction Wheel 



necessary lo the upper portion of the case in which interference o[ 
the two streams and much eddying are possible, all of which is ob- 
viated in the the design, shown in Fig. 317. The writer knows of 
no experiments which show conchisively that such loss actually 
occurred* More information is needed a!ong this line than is now 
accessible to the engineer. 




Fig. 317. — Double Horizontal Tiir!>Jne In Closed Penstock ^ Dayton Globi IroJ* 

Worki Go.) 




Fig. 318.— Flan- 

Fig* 319 is a cross-section of a double unit of the Samson tur* 
bine, manufactured by The James Lcffel and Company of Spriof 
field, Ohio. This shows a design in which careful attention i* 
given to the maintenance of a uniform and slowly decrcasinf ^e- 
loKrity frosi the time the water reaches the wheel until it passes 
from the common draft-chest into the draft-tube below. 



Some Installations of Horizontal Water Wheds. 



5^7 



257, Some Installations of Multiple Tandem Horizontal Wheels, 

J— Two double units of the wicket gate type, similar to the double 
pnits shown in Fig. 315, are illustrated by Fig. 320, These turbines 
%vere manufactured by The Daytosi Globe Iron Company of Day- 
ton, Ohio, and are shown with the tipper portion of the case removed 
teo that the arrangement of the wheels and the gate mechanism are 
learly visible. The gates are moved by a cylindrical ring to which 



r 




F1& S19, — Double Horizontal Turbine for Open Penstock. (James Leftel & Co.) 

each gate is attached independently. The ring is moved by the 
link connecting the gate ring to the governor rod which, by its ro- 
tating, opens or closes the gate as the power needed requires. 

Two double units with cylindrical gate, as manufactured by The 
S, Morgan Smith Company of York, Pennsylvania, are shown 
in Fig_ 321, The bulkhead casing and the coupling to which the 
machinery to be operated must be attached, are shown at the left. 
In this case the governor rods have a horizontal movement, the 
upper rod moving backward and the lower forward in order to 
open the cylinder gate. 

Figs. 322 and 323 show a section throitgh one of the main units 
and a plan of the power house and turbines of The Southern Wis- 
consin Power Company now under construction at Kilbourn, Wis- 
consin, on the designs and under the supervision of the writer. 
This plant consists of four main units, each generator having a 
capacity, at full load, of 1650 kilowatts and an overload capacity 
of 25 per cent. Each unit is direct-connected to six 57* turbines 
now under construction by The Wellman-Seavcr-Morgan Com- 




.i-L 



Some Installations of Horizontal Water Wheels. 




5^9 






e 



e 

-a 






& 

i 



530 



Arrangements of iht Reactioo WheeL 






pany of Cleveland, Ohio. Each turbine unit is set in i separate 
penstock controlled by three independent sets of gates. The four 
center wheels discharge in pairs into common draft-tubes, while the 
two end wheels have independent draft-tubes. All of the hearings 
within the flume are accessible by independent wrough iron man- 
hole casings. 

Fig. 324 shows four pairs of 45" Samson horizontal turbines ma:]- 
ufactured by The James Leffel and Company of Springfield, Ohia 
These wheels have been installed for The Penn Iron Mining Com- 
pany of Vulcan, Michigan, where two such units are now in opera- 
tion. Eight similiar units» designed to deliver 1400 H, P, under H 
foot head| are now under construction by The James Leffel and 
Company and are to be installed in the plant designed' by the 
writer for The Economy Light and Power Company at Dresden 
Heights, Illinois, the general arrangement of which is shown by 
Fig, 350. 

When the head increases above 20 or 30 feet, it may become de- 
sirable to convey the water frorn the head-work by means of a 
closed penstock as shown in the case of the plant of The Winnipeg 
Electric Railway Company (See Fig, 340), 

In this plant are shown four wheels in tandem, direct connecied 
to a generator. The bell-mouthed entrance to the penstock should 
be noticed, also the air inlet pipe which is designed to admit ihc 
air into the penstock when the same is to be emptied, and to acirok 
the water gradually and without shock when it is again fillcd| 
When the head becomes still higher the closed pemstock becomes ii 
perative as in the case with The Shawinigan Water and Power Com-J 
paoy's plant shown in Fig, 33S where a head of 135 ft. is utitiKdj 
Similar arrangements and connections for single and double wheefsl 
with penstock are those of The Dodgeville Electric Light and[ 
Power Company* shown in Fig. 337, and that of The Hudson River j 
Power Company's plant at Spier's Falls, as shown in Fig. 335. 

The plant of the Nevada Power and Mining Company sbown i^\ 
Fig. 341, involves tangential wheels operating with needle nouki 
and discharging freely into the tail race below. 

In the selection and installation of reaction wheels a con- 
siderable latitude in the choice and details of arrangement is r^^si* 
ble and it is only after a careful examination and consideration of 
all the conditions of installation that the correct size, speed, and [ 
arrangement of the wheels can be obtained. Numerous failuf^^ 
more or less serious, in the past have fully shown the fact that 




Some iDStallations of Horizontal Water Wheels. 5^' 




S2» 



Arrangement o£ the Reaction WheeL 




524 



Arrangement o£ the Reaction Wheei 



this work demands the most careful attention and investigation of I 
the engineer and should be attempted only after the most thor-| 
ough study and mature deliberation. 

358. Unbalanced Wheels, — In installing horizontal wheels it is! 
usually desirable to use them in pairs with two, four, six or tlghil 
turbines in tandem. It is, of course, possible to introduce an oddl 
number of wheels and this is frequently done where it seems to be 
desirable* There is an advantage is an even number of wheels tor 
in this case the wheels may be, and should be, so arranged as to 
balance the thrust by the union of a right hand and left hand whe«l 
in eacli pair. Where an odd number of wheels is introduced, an 
unbalanced condition arises which can only be taken care of by a 
thrust-bearing which, at the best, is an additional complication 
cj^ten unsatisfactory and should be avoided if possible* 

There is another cause of unbalanced condition which mty be 
here mentioned. If a pair of wheels is so joined tog^ether as to 
use a common draft-tube then, on starting the wheels the vacmim 
formed in the draft- tube is common to both wheels and therefore 
balanced. If, on the other hand, the wheels have separate draft- 
tubes, when the wheels are started a partial vacuum is commonly 
created in one of the draft- tubes in advance of the other, or even 
when the wheels are in operation the vacuum in one draft-tube is 
not as gfreat as in the other, creating thereby a thrust in one di- 
rection or the other which must be balanced by the connection of 
the two draft -tubes by an air pipe or must be taken up by a thrust- 
hearing as in the case of a single whceL 




CHAPTER XXL 

THE SELECTION OF MACHINERY AND DESIGN OF 

PLANT. 

250. Plant Capacity. — The selection of machinery for a power 
ant depends upon numerous conditions. In the first place, for 
rmanent and constant operation, the machinery must be so 
lected that its total capacity shall be great enough to take care 
the maximum load and have at least one unit in reserve so that 
it becomes necessary to shut down one unit for examination or 
pairs, the plant will still be capable of carrying the maximum 
ad for which it was designed. 

The desirable reserve capacity of any plant depends on the con- 
ngencies of the service or the degree of liability to disabling acci- 
ent involved in the operation of any plant, and on the relative 
ost of such reserve capacity and the damages which might be sus- 
ained if the plant should at any time become disabled as a whole 
►r in part and incapable of furnishing all or any part of the power 
or which it was designed. In many manfacturing plants the occa- 
sional delays caused by the entire suspension of power on account 
rf high or low water, or for the necessary repair to machinery, are 
*ot serious if cheap power is available for the remainder of the 
ear. For the operation of public utilities, and the furnishing of 
&ht and power for diverse municipal and manufacturing purposes, 
>e matter becomes more serious and necessitates a sufficient du- 
'cation of units to practically assure continuous operation. 
Por paper mills and other manufacturing purposes water powers 
- utilized in which the head and consequent power is practically 
•stroyed during high water conditions. For continuous and un- 
^errupted service such powers are available only with auxiliary 
^'Wer that can be used during such periods. In the same manner 
s^rve capacity may be unnecessary, desirable or absolutely essen- 
^' as the importance of maintaining uninterrupted power in- 
^ses. 

^Co. Influence of Choice of Machinery on Total Capacity. — A 
^dy of the week day load curve of The Hartford Electric Light 
S2 



5^6 The Selection of Machinery and Design of Plant 



Company as shown by Fig. 257, page 422, will show that the load 
for December, 1901, represents the maximum load which that plant 
was called upon to carry during the year, and, consequently, was 
the maximum load for which the machinery must have been se- 
lected, A considerable variety of unit sizes w^ould be possible 
which would fill the requirements of this load curve to a greater 
or less extent The maximum or peak load shown in Decembefi 
1901, was about 3,000 k, w. If a single machine were selected of 
3,000 k w, capacity for regular operation, then, in order to have 
one unit in reser\^e, it would be necessary to purchase two 3,000 
k. w. machines or a total capacity of about 6,000 k. w. It on the 
other hand, machinery should be purchased with units of joo 
k» w. capacity each, it would be necessary to have six of such units 
in order to carry the maximum load of 3,000 k. w*, and a sevenih 
unit of 500 k, w. capacity would be all that would be needed for the 
reserve. This would give a total capacity to the plant of 3,500 k, w., 
giving the capacity of the machine purchased some 2,500 k. w. 
less than the plant first discussed. 

261* Effect of Size of Units on Cost — The cost of machinen- ii 
not in direct proportion to its capacity. The larger machincn- is 
somewhat less in price per kilowatt capacity than the smaller ma- 
chinery. Hence the cost of the last plant suggested would be more 
than 35/60 of the cost of the first plant On the other hand, the m-^ 
s t alia t ion of such a large number of units complicates the plant an 
is undesirable. For this plant it would therefore be desirable 
select five units of 750 k. w. capacity each, or four units of to 
k. w. capacity each, giving in one case a total plant capacity 
3,750 k. w, and in the other case of 4,000 k. w. 

A plant having units of 750 k, \v. or 1,000 k- w. capacitj' ead 
would have a less total kilowatt capacity and, consequently, a le 
first cost compared with a plant having units of 3.000 k, w. capacity 
Such a plant would also have a less number of units and coo* 
quently less complication in the arrangement than a plant haviii 
units of 500 k, w. capacity. 

262, Overload.^ — In the above consideration no mention is miA 
of overload capacity. The ordinary direct-current machinery 
be operated at about 25 per cent overload for short periods ol | 
haps one hour at a time without danger to the machinery, Altei 
nating machinery can be operated at 50 per cent, overload at sin 
times or at 25 per cent overload for two hour periods. In < 
quence of this condition it is frequently possible to purchase 1 



Economy in Operation. 527 

nery of considerable less capacity than the total load would in- 
ate, depending on the overload capacity of the machine for short 
"lods of maximum load. Unless, however, the estimated load 
•ve covers all possible contingencies for maximum power it is 
lirable to retain this overload capacity as a provision for a second 
idition which has not been fully covered in the estimate of the 
ly load curve; or, in other words, it is desirable to retain the 
jrload capacity as a factor of safety. 

{63. Economy in. Operation. — A second matter that needs the 
eful consideration of the engineer in the selection of machinery 
the question of economic operation under variation in load. A 
erence to the efficiency curve of most machines will show that 
machine will operate most efficiently at some particular load, 
lally some .75 to full load, and will perhaps give the best results 
from .75 to 1.25 load, or to 25 per cent, overload. It therefore 
:omes important to so select machinery that it will operate effi- 
ntly at all conditions of load. 

Kn examination of the load curve of The Hartford Electric Light 
mpany for the full week day load in March, June, September 
i December, will show that for securing the most efficient results 
all times in the day, and at all times in the season, units of 500 
w. capacity would apparently be the best. Such units would 
:e care, efficiently, of the minimum loads that occur at 6:00 
M., between 12:00 and i :oo P. M., and at about 7:00 P. M. At 
:h times one of these units would operate efficiently; but in 
)st cases the period at which it could be operated singly would 
for a few minutes only, or perhaps for an hour at the most, when 
t additional unit would have to be cut in. A 750 k. w. generator 
mid operate with almost as great an efficiency at these times and 
would, with its overload capacity, take care of the load for a much 
eater period of time each day. The 1,000 k. w. machine would 
rhaps fulfill these requirements even to a greater degree. While 
would be less efficient at the minimum point of the load, it would 
ive the advantage of operating singly for a much wider range of 
id and the additional advantage that, as a rule, the larger the ma- 
ine the higher the full load efficiency curve. 

The complications resulting from the numerous machines, and 
i losses entailed thereby, have also to be considered and must be 
iefully weighed in this connection. 

Hbe circumstances of operation and many local conditions, which 
^rtain particularly to the plant in question, must be weighed in 



Sa8 The Sekction of Machinery and Design of Plant 



k. 



connection with the selection of this machinery- There is n<j dcS 
nite law by which the selection of machinery for any plant ad 
be reduced to an exact science, and several combinations of mi- 
chinery are possible in almost any plant and will give reasomk 
satisfaction. 

In the above discussion only units of a uniform capacity hail 
been considered and it is usually desirable, other things being cqiK 
to have similar machines so that a minimum number of rep 
and duplicate parts may be kept in stock. On the other haniiij 
long, low night load is probable, it may be desirable to insialii 
or more units of a capacity suitable to carry such load efficienik | 

264. Possibilities in Prime Movers. — A third matter for 
careful consideration of the desigfnin^ engineer is the possibiW 
of a prime mover that is to be used for operating the machines i 
question. If a steam or gas engine is to be used as the moti^ 
power, there is a w^ide range of selection in speed, capacity, ad 
economy of such machinery, and, as a general rule, the prime racut 
may be selected to conform to the generator or other machine ill 
is to be operated thereby* In the selection of ^^-ater wheels foT 
prime movers the conditions are radically different and the selection 
of the size and capacity of the units to be operated is often modi- 
fied or controlled by the water wheels and the conditions unj 
which they will be obliged to operate. 

In the selection of the water wheel one of the most importam 
matters is the head and the range of heads under which the wheel 
will he called upon to operate. While it is possible to select a whc 
so that it will operate at almost any reasonable speed under a < 
siderahle head, yet the capacity or power of the w^heel rapidly '1^" 
creases in amount with the speed, and if the speed be too hisli i^ 
will he necessary to join two or more wheels in tandem in order! 
furnish the power necessary to operate the machinery selects 
This is perfectly feasible and is done in a great many eases. 

365. Capacity of Prime Movers. — It is important to note that i 
the generator or other machinery to be operated is to be operator 
under overload conditions, the maximum powder to be generatei^ 
must be kept fully in mind in the selection of a prime mover 
the case of steam engines, these engines can be commonly opemte 
under overload conditions. They are usually rated at their m<3i 
efficient capacity and can sometimes be operated to 50 per cenil 
above their normal rating, although their economy under such 
ditions is apt to materially decrease. Gas engines, on the othe 



Power Connection. g ^ 

and, are commonly rated at very nearly their full capacity aiid 
hence tlie machinery which they are to operate can be operated only 
to about the normal rated capacity of the engine. 

Water wheels are commonly rated in the catalogues of manu- 
, facturers at very nearly full gate and consequently at full power. 
In some cases they are rated at abotit seventh-eighths gate so that 
^ a small margin of additional power is availalble. In the selection 
I of a water wheels therefore, it is important that a careful study 
I be made of the actual power that the wheel can generate under full 
|i g^te and at minimum head. This should be sufficient to operate the 
I machmery at its niaximum load, 

266. The Installation of Tandem Water Wheels. — ^The installa- 
U±ion of t%vo wheels set tandem, either horizontally or vertically, 
nnd directly connected with the machine by a common shaft, is 
[very common and this may be increased to four, six, or occasionally 
I to eight turbines. Every additional machine, however, involves the 
f introduction of increased diameter in the shaft, of additional bear- 
ings Avhjch must be set and held in alignment, and a compHca- 

■yjon in the design and construction of the machinery which should 
Pbc avoided wherever possible. The excuse for the attachment of a 
numDer of turbines in tandem arrangement, and the com- 
plexity of the plant of water wheels installed, lies in the sim* 
plifi cation of the machinery to be operated by them, and in the de- 
sign and arrangement of other portions of the plant. The extent 
to which the application of any principle is to be carried is a matter 
of Judgment and can be answered only by experience and the con- 
sideration of all of the conditions involved in each particular case. 

267, Power Connection.^\Vith the turbine, as with every other 
prime mover, it is important to convey the power to the machine 
or machinery to be operated as directly as possible. The turbines 
should be connected as directly as possible to the machinery to be 
driven without any nnnecessary intervention of gearing, shafting, 
bearings, belts, cables, or other still more complicated methods of 
power transmission. Every shaft, every gear, every belt, every 
bearing and every other means of transmission that intervenes be- 
tween the power generated in the wheel and the machine in which 
the power is to be utilized means an extra loss and a decrease in 
the efficiency of the plant. The machine to be operated should, 
therefore, whenever practicable, be direct connected to the slmtr 
of the turbine instead of being connected with the turbine by any 
intermediate mechanical means. (See Figs, 310, 314 and 322- 



330 The tielecUon of Machinery and Desiga ot PlaaL 




Various Methods of Connection, 



531 



£t connection of machinery and turbine involves a careful selcc* 
of both machinery and turbine so that both will work satis- 
rily at the same number of revolutions per minute. This 
(Cntly involves extra expense that may not be justified in plants 
lany purposes, 

acr methods of connection or of power transmission are, 
fore> frequently necessary* With many low head installations 
k connections are impracticable for a number of reasons, 
itmes various machines with diverse revolutions are to be 
U by the same wheel and the revolutions of the turbines in* 
d must differ from some or all of the machinery to be operated 
jomc form of connection other than the direct must be used* 
■where the importance of the plant makes it desirable to use di- 
^onnection, it frequently happens that a single turbine gives 
sufficient power at the speed desirable for connection to a 
Ine of the desired capacity. Under such conditions it is nec- 
f to unite two or more turbines in order to generate sufficient 
r for the purposes for which the plant is to be designed. Tlie 
sfty of using a large number of turbines in a single unit may 
rise to very long shafts and a large number of bearings, and 
iss due to such an arrangement is sometimes considerable, and 
^rly arranged will be almost or quite as inefficient as gearings 
ihafting well maintained. 

w Various Methods of Connection in Use. — ^The most common 
of turbine used is a single vertical turbine, connected by a 
jed crown gear and ^pinion to a horizontal shaft. Several of 
tiirbines are commonly coupled up to the same shaft and may 
i in a single or in separate wheel pits. Such types of installa- 
are sho%vn in Figs, 329 to 334, Fig. 325 shows the turbine 
►ss in the plant of The Oliver Plow Works at South Bend, 
ma, installed by The Dodge Manufacturing Company, The 
Igement of the wheel is quite similar to that illustrated by 
334, Three or four vertical wheels Jire here each connected 
^ear and pinon with a horizontal shaft, w^hich, in turn, is con- 
kl to an electric generator. In all such cases more or less 
[y is lost in transmitting the power throtigfh the gearing and 
ITQUS bearings to the generator. Sometimes it is found desir- 
tiot to connect the generators directly with the main shaft, 
© connect the generator or other machines to be operated by 
^wer plant by belting them to driving pulleys attached to the 
[horizontal shaft, as shown by Fig. 326, which shows the power 



jj 



53a The Selection of Machinery and Design o£ Plant. 




Vairous Methods of Connection, 



S33 



plftat of The Trade Dollar Mining Comp*iny near Stiver City, Idaho, 
This, however, introduces another source of loss through these 
b«lt5 but possesses a certain flexihility due to the abihty to thereby 
drive various small units at a variety of speeds by the simple process 
of changing the diameter of the pulleys used to drive such machin- 
ery. Sometimes rope drives can be used to advantage in place of 




Fig- 327, — Haruesa and Driving Sheaves^ Soutliweat Missouri Light Oo,, 

belts. This is especially true where the distance is great or the 
alignment other than direct. Examples of such connections are 
shown by Figs, 327 and 328, 

Direct connected plants are shown in Figs. 310, 314, 322, 335, etc. 

269* Use of Shafting. — A shaft connecting a machine to a prime 
tnover, or imposed in any manner in any power transmission, must 
lie carefully designed and constructed. It must be carefully aligned 
and have its bearings carefully adjusted. Each bearing may be con- 
sidered as a point in the alignment of a shafts and, as two points 
determine the direction of a straight line, it will be seen that each 
additional bearing is objectionable for it increases the difficulty of 
Staining and maintaining a satisfactory alignment. When more 
than two bearings are used each must be brought and maintained in 



* Dod^e Manufacturing Co., Mlsbai^ aka, Ind, 



534 Tht Seleciion of Machinery and Design ol Plant 



the best practicable alignment, both honzonally and vertically. All 
bearings must be of sufficient size that the limit of bearing pres- 
sure shall not exceed good practice and they must be sufficiently 
adjustable so that the shaft shall have as complete and uniform bear- 




Ftg. 323. — Flan Showing Harness,. Rope Drive una Jaeksliaft. Sotitbw«^ j 

Missouri Light Co.* 

ing as possible over the entire surface of the box Boxes and bear- 
ings must be arranged for satisfactory lubrication so that m^^ 
the hardest service they will not become unduly heated. In ortftf 
to secure good results the best class of workmanship is nec«ssirf 
and it is also necessary that the plant shall be carefully and prop- 

*Dodge Manufac^turliig 



r The Wheel PiL 535 

crly maintained, A poor shaft, running in poor boxes ^ poorly 
aligned, may consume most of the power generated. Shafting, to 
be reasonably satisfactory, demands frequent and proper inspectioUj 
constant lubrication^ and proper maintenance or it will soon become 
a source of great energy loss» 

270, The Wheel Pit. — The wheel is usually set in a chamber 
called the wheel pit, flume, or sometimes the penstock, which is 
connected with the head-race from which it can be separated by 
suitable gates. 

The wheel pit in the smaller plants has commonly been con- 
structed of timber but in the larger plants is usually built of a more 
substantial character, — of concrete, plain or reinforced, stone or 
iron. 

Open pits are commonly used for heads up to 18 or 20 feet, and 
may be used for considerably higher heads; however, for higher 
heads, closed flumes of reinforced concrete or steel are commonly 
used, and such construction is usually connected with the head- 
race by metal, wood or reinforced pipes, to which the term penstock 
is commonly applied. This latter form of construction admits of 
the use of wheels with heads of almost any height 

A number of wheels can be set in the same wheel pit, and are 
commonly so set, especially where they are used together to 
operate one machine* It is frequently desirable, however, to sep- 
arate the turbines and set them in separate pits so that one or 
more wheels can be shut down at any time without interfering 
with the operation of the plant. The exent to which this arrange- 
ment is carried is a matter of policy and depends upon a variety of 
conditions which the engineer must settle for each particular case. 

271. Turbine Support. — The arrangement and construction of the 
wheel pit must be such as to furnish a proper support for the tur- 
bine in order to secure satisfactory operation. In many of the 
earlier plants, the wheel pits were built of timber, with the turbine 
case resting directly on the timber floor, which was often improp- 
erly supported. The result of such conditon has been that the tur- 
bines settle out of alignment and much energy is expended in un- 
due friction in the transmitting mechanism. The floor or founda- 
tion on which the wheel case rests should be of a substantial char- 
acter and of such a nature that it will not readily deteriorate and 
allow the wheel to settle. It is usually desirable to support the 
wheel by a column directly below the wheel case, which should rest 
upon substantial foundations below the bottom of the tail-race. 




536 The Selection of Machinery and Design of Plant 1 

(See Fig* 331) In all events settlements and vibrations must be 
prevented or reduced to a minimum in order to eliminate one of tlic 
very important causes of loss which is frequently encountered in 
water power plants. In many cases, due to defects of this kimi 
water power plants are givnig efficiencies of 50 per cent, and below, 
where 75 or 80 per cent, should be obtained. 

272, Trash Racks. — The water entering the wheel pit from tht 
head-race commonly passes through a trash rack consisting af fiar- 
row bars of iron, usually 14" by 3" in dimension, spaced iW^ ^^ ^ 
between and reaching from above the head- waters ^o the bottoiti d 
the wheel pit, the purpose of which is to strain out such floatmf 
matter as may be brought by the current down the head-race and 
which, if not taken out at this point, might float into the wliceb 
and if large and heavy enough, might seriously injure the same 
These racks have to be raked or cleaned out at intervals depending 
on the amount of leaves, grass, barks, ice or other floating matter 
in the stream. In water power plants on some streams where largt 
amounts of such floating matter occurs at certain seasons, it »s 
sometimes necessary to keep a large number of men constantly 
at work keeping the racks clear. 

Tile accumulation of material on the racks will sometimes shut 
off the entire flow of water if attention is not given to keeping them 
clear; hence it is sometimes necessary to so design the racks and 
their supports that they may sustain the entire head of water- 

The racks are usttally made of bar iron held apart by spools l)^ 
tween each pair of bars and held together by bolts passing through 
the spools and joining together such a number of bars as may I 
convenient for handling. The spools should usually be placed neil 
the back of the bar so as to allow the rake teeth to pass readilf«| 
.The rack should be situated at an angle so as to afford facifiti«i| 
for raking. The deeper the water, the greater should be tk iff 
clination, as with long racks, and especially with high velocities, thij 
clearing of the racks becomes more difficult 

Chain racks and automatic mechanical racks have been attemptra| 
but without satisfactory results. 

Where trouble occurs from ice, involving much winter wortt rtj 
is frequently desirable to cover the racks with a house in order t<^ 
protect the workmen. 




CHAPTER XXIL 

EXAMPLES OF WATER POWER PLANTS, 

373. Sterling Plant — A rear elevation (Fig, 329) of the plant 
wtiich was designed by the writer for The Sterling Gas and Electric 
Company of Sterling, lUinois, shows three 50" vertical Leflfel wheels 
connected to a common shaft by beveled gearings. 

The genera! type of harness used is fully shown in the plan and 
elevation and needs no further description. 

This plant is located on the Steriing race and is next to the last 
plant on the race on the Steriing side of Rock Riven (See Fig. 345,) 
The head developed at this plant is about 8 feet, and the power of 
each wheel is about 115 horse power. Each wheel is set in an inde- 
pendent wheel pit which can be closed by means of a gate, as shown 
in Fig. 332. In order to make repairs on any wheel without inter- 
fering with the other wheels, the wheels and harness are well sup- 
ported from the foundation, a very essential condition for perma- 
nently maintaining a high efficiency. The discharge pit is of ample 
size, so that the velocity with which the escaping waters leave the 
draft tube is reduced to a practical minimum. A rack, to keep 
coarse floating material from the wheel, is placed in front of the 
penstock and is shown in Fig. 331, in section, and in Fig* 332, 
in partial elevation. The shaft otf this plant is extended into the 
adjacent building and to it are belted the generators which supply 
electric current for light and power purposes in the city of Sterling. 
An engine is also connected to this main shaft and may be utilized 
in case of extreme low water conditions, where sufficient water for 
power is not available, or for flood conditions where the head is 
practically destroyed. 

274. Plant of York-Haven Water Power Comparfy. — ^Figure 333 
shows the arrangement of the power station of the York-Haven 
Water Power Company on the Susquehanna River at York, Pa, 

The power house is 478 ft long and 51 ft wide. The head-race 
is 500 ft long and of an average depth of so ft. The wheel pits are 
19 ft* deep and extend the entire width of the power house, open- 





i 



lant of the Sterling Gas and Electric Light Co* 539 







6 






^ be 

Q B 

a 

8 






540 



Examples of Water Power Plants 




H|J i yyipnny ill| yHj iji^ .1 ff i f i 



k 

^ 

i 






I 



^ ^ C T / O N 
F1». S31.— Wheel Pit, SUrllng Ga* and Electric Ught Oo.'a Plut 



Plant of the Sterling Gas and Ekctric Light Co. 54^ 




3 

s 






54- 



Examples of Water Power Plants, 



mg to the forebay. They are protected by iron racks and are made 
accessible by lar^c head-gates of structural iron which weigh about 
eleven tons each. 




Fig. 333 — Plant of York Hfiiren Water Power Co, 

(Electrical Engines.) 

Each pit contains two 78.5'' inward flow ttirbines, hung fr< 
spring bearings just above the runners. The turbines are set on t 
floor of the pit and arc about 6 ft* above the lower water mark. 

The draft tubes are 10 ft.^long and extend well under water The 
net head under normal conditions is about 21 ft. Float ^it^c^ ^ 
the switch board show at a glance the height of head and tail 
water. 




Plant of South Bend Electric Company. 543 

The turbines were built by the Poole Engineering Company of 
Itimore, Mr., and are rated at 550 H. P. each, or 1,100 H. P. per 
r. 

rhe turbines are oi special design, the buckets being made of 
issed steel. The shaft extends vertically from the turbines to 
rel gears above the main floor and each is encased in a cast iron 
»e to protect it from the action of the water and to secure long- 
ty both to the shaft and to the bearings which retain it in line. 
The present installation consists of ten pairs of turbines with 
generators, equipped with Sturgess and Lombard governors. 
The turbine bearings are supplied with oil from a gravity tank 
ated on the switch-board gallery . 

The generators are S. K. C, three-phase, 60 cycle alternators, 
ed at 875 kilowatts, and generate a 2,400 volt current. The nor- 
l speed of the generators is 200 revolutions per minute. Two 250 
W., 125 volt, S. K. C, compound-wound, direct-current exciters 
nish the exciter current to the generator fields.* 
75. Plant of South Bend Electric Company. — Figure 334 shows 
plant of the South Bend Electric Company at Buchanan, Mich- 
n, built in 1901. 

Tic dam, which was constructed in 1895, is of the gravity type, 
It of wood, with two rows of sheet piling below and one above 
It IS about 400 feet long, and affords an average head of 10 feet, 
is is estimated to furnish a minimum of 2,000 h. p. for from 
r to six weeks in a year, while the maximum will reach 5,000 h. p. 
an average, 2,500 h. p. is available for about three months and 
X) h. p. for the remainder of the year. 

The power house, placed a short distance below the dam, is 273 
t long and 40 feet wide. It is built of stone, with concrete foun- 
ions, and slate roof. It parallels the river so that the water from 
turbines is discharged directly into the same. The regulating 
es are seven in number, and are operated by racks and pinions. 
The water wheels are Leffel turbines of 68 inch vertical type, 
• h. p- each. They are geared to a line shaft, which extends nearly 
whole length of the building, and to the end of which the genera- 
is coupled. A 40 inch vertical LeflFel wheel is used for driving the 
:iter, which is belted to an intermediate shaft, driven by gears, 
e line shaft is divided into three units, so that either four, seven 
ten wheels can be used for operating the generator, depending 

See Electrical World, vol. 49, March 2nd, 1907. 



Spier's Falls Plant Hudson Water Power Co. 



545 



n the load carried. In addition, the gears on the line shaft can 

:hrawn out of mesh, so that any water wheel can be repaired if 

essary. The plant is governed by two Lombard water wheel 

ernors driven from the line shaft. 

. 20 ton hand-operated crane serves all the apparatus in the 

ding. 




335. — ^Plant of Hudson Water Power CJo. Spier's Falls Plant Double 
Horizontal Turbines in Steel Penstock. Central Discharge. (E}Qgine- 

ering Record.) 



he generator is a 1,500 k. w., 60 cycle General Electric revolving 
I type alternator supplying three-phase current at a pressure of 
o volts. The switch-board and transformers are located at one 
of the building. There are no high tension switches at the 
^cr house. 

he power is largely transmitted to South Bend, Indiana, a 
ancc of 16 miles, where the company has a steam power plant 



Si6 



Examples of Water Power Plants. 



which is always kept in such condition as to be put into immediate 
operation. It is used, however, only in case of extreme low water, 
at times of a heavy peak, or in case of accident to the transmissiciii 
line. The steam power house is used as a stsb-station and distrib* 
uting point.* 

276* Spier Falls Plant of The Hudson River Power Transmission 
Company^ — ^A cross section of the Spier Falls Power house is sho^-u 
in Fig. 335* A head of 75 feet, for operation of this plants is derivtil 
from a granite rubble, ashlar- faced, masonry dam across the Hud- 
son River between Mount McGregor and the Luzerne Mountam 
The dam consists of 817 feet of spill w^ay section, the remalndexy 
of the dam, 552 feet, being- built about 12 feet higher, Wata 
is admitted through arched gateways to a short intake canal dc-^ 
signed to carry 6,000 cubic feet per second with a velocity of three j 
feet per second. This canal distributes the water to ten 12' circa 
steel penstocks %vhich lead about 150 feet to the wheels. 

The power house is divided into three parts with the transfonner j 
and switchboard room in one end, the wheel room and generatoi 
roon. being formed by a longitudinal partition wall extending^ th^ 
length of the building, with traveling crane in each. 

Each unit consists of a pair of 42" or 54" cased S. Morgan Smiih 
wheels^ governed by Lombard and Sturgess governors and directj 
connerted to 2,000 and 2,500 k* w. 40 cycle, three-phase revolvinf 
field generators, built by The General Electric Company, 

The transformer room contains sc\ en 670 k. w. and thirty %J 
k. w* General Electric air cooled transformers. 

The power is distributed to Glen Falls, Schenectady, Sarata 
Springs and Albany, f 

377* Plant of Columbus Power Companyp — The plant of th 
Columbus Power Company is shown in Fig. 356, It is situated *^9^ 
the Chattahoochie River just beyond the limits proper of tlte cityj 
of Columbus, Georgia, at a shoal known as Lovers' Leap. At tiiC 
point a dam of Cyclopean or boulder concrete with a cut stone sp 
way surface was erected giving a head of 40 feet. The length of ^1^*^ 
dam is 975 feet 8 inches* with a spillway 728 feet long* 

The power house is located at one end of the dam» so that no p*^"] 
stocks are necessary. This applies to power house No. i. PDwct 
to drive the plant of The Bibb Manufacturing Company is ^^'M 

•(See Electrical World and Engineer. May 30, 1903 and July 14. IW 
tR^ Engiiieering Record ^ June 27th, 1903. 



Plant o[ Columbus Power Co, 



547 



tiished from power house No. 2, being^ transmitted to the mill by a 
rope drive system. The power house is supplied with pressure 
water by means of penstocks let through the bulk-head wall, which 
extends from house No. i to the river bank. In both cases the 
tail water is discharged into the excavated river bed beneath the 
power houses. Power House No* i is designed to develop 6,000 
h, p. ia six units, and No* 2 about 3,ocX3 h. p, mainly in two umta. 




p mw Jm J ^ J M t.T^Jyf T J^^ i ; il 'i'P^ 'ljfc » 



Fig. 33S. — Plant of Columbtis (Gaj Power Co. Double Horizontal Turbines 
In Open PenBtock. (EnirtneeTing News.) 



Power house No. 1 is 137 feet long and 52 feet wide. It rests on 
heavy stone foundations, the up-stream portions of which form the 
heavy bulk-head which is pierced by six large openings for plant No, 
I, by a smaller opening for the exciter units and a larger one for 
the penstock leading to power house No. 2. 

The openings for power house No. i are short flumes or chambers. 
The back end of each of the wheel chambers is closed with a 
heavy plate or bulkhead of cast iron and steel separating the wheel 
chamber from the generator room. The racks are of the usual con- 




548 Examples of Water Power Plants. 

struction and are supported on a framework of I-beams, giring 
them an inclination of about 12** with the verticaL The gates to the 
wheel chambers are of timber and are raised by hand bj means 0(1 
rack and pinion. 

Each of the main wheel chambers Contains a pair of horizontal 
39 inch Hercules turbines, which discharge into a common draft 
tube. The center line of the wheels is 15 feet below normal head 
water level and 25 feet above normal tail water leveL Under the 
total head of 40 feet, each pair of wheels develops 1,484 h. p. at 200 
r. p. m. The draft tubes are 7% feet in diameter at the turbine cas- 
ing and 10 feet at the discharge end. 

Each pair of wheels is direct connected to a two-phase alternator 
built by the Stanley Electric Manufacturing Company. Each ma- 
chine has a rated capacity of 1,080 k. w. at 6,000 volts and driven at 
200 r. p. m. gives current at 60 cycles. Each is connected to the 
wheel shaft by a flexible leather coupling. 

There are two exciters directly connected to a single 18 inch 
Hercules wheel. Each exciter is of the Eddy type, having a capac- 
ity of 60 k. w. at 75 volts and running at 450 n p. m. The exciters 
are under the control of mechanical governors-* 

278. Plant of The Dolgeville Electric Light and Power Ca— In 
Fig. 337 is shown the plant of The Dolgeville Electric Light and 
Power Company at High Falls, New York, on what is now known 
as the Auskerada River. 

The dam is built of limestone masonry. The height at the spill- 
way is 20 feet, with each abutment 6 feet higher. The total length 
is about 195 feet. The width at the top is 7 feet and at the bottom 
26 feet. The upstream side is perpendicular, the downstream side 
being curved in order to properly receive and discharge the water. 
The head gate, 12 ft square and built in two sections, is fitted with 
a by-pass gate to relieve the pressure when filling the flume. The 
steel flume extends from the head gate to the power house, 520 feet 
away. This flume is 10 feet in diameter, and is made of % inch 
steel plate, all longitudinal seams being double riveted. Just out- 
side the dam is a vent pipe which assists in relieving the flume 
from any sudden strains. 

There are two 36 inch horizontal Victor turbines, each direct 
connected to one 450 k. w. 2,400 volt two-phase Westinghousc gen- 

• See Electrical World and En^neer. Jan. 23, 1904 «r Bng. Record, Jin. 1^ 
1904. 



Plant of Dolgeville Electric Light and Power Co, 549 




5 so Examples of Water Power Plants. 

erator. Each of these wheels will develop 600 h. p. at 300 r. p. m^ 
under the working head of the water, which is 72 feeL They are 
mounted in cylindrical steel casings, and discharge downward 
through draft tubes, which extend a few inches below the sur- 
face of the tail water. Each wheel is supplied with a Giesler elec- 
tro mechanical governor.* 

279. Plant of the Shawinigan Water and Power Company.— The 
power plant of the Shawinigan Water and Power Company is lo- 
cated on the St. Maurice River, Canada, at a point about 21 miles 
from Three Rivers, 90 miles from Quebec, and 84 miles from Mon- 
treal station. Fig. 338 shows a cross-section of their power station. 

The St. Maurice River has a total length of over 400 miles, and is 
supplied from a great many lakes and streams, the drainage area 
being about 18,000 square miles. The water flow is very steady 
throughout the year on account of the dense forest covering this 
area, and is in the neighborhood of 26,000 cu. ft. per second, seldom 
going below 20.000 cu. ft per second. At the crest of the falls the 
water flows over a natural rock dam and then down over the cas- 
cade, making a fall of about 100 feet, then on in a narrow gorgt 
through which the water rushes swiftly and in which there is a 
further fall of 50 feet 

The intake canal is 1,000 ft. long, 100 ft wide and 20 ft deep. Its 
entrance from the river is located in a rather rapidly flowing stream 
at the crest of the falls where the water is 20 feet deep, for the reason 
that at times of rather high water, when the ice is flowing out d the 
river, the current is expected to carr\- the ice past the mouth of the 
canal. Tlie end oi the canal where it comes out at the face of the 
hill is closed by a concrete wall from which the water is led through 
steel penstock pipes down to the power house 130 feet below. 
The concrete wall or bulkhead in the canal is 40 feet in height. 
about 30 feet in thickness at the bottom and 12 feet at the top. 
On top of this wall are set hydraulic cylinders for lifting the head- 
gates and ov top. covering the cylinders, is a brick gate hous^ Tlie 
steel penstocks are 9 feet in diameter. 

The electrical apparatus was supplied by the Westinghouse Elec- 
tric & Maruifac::ring Conipanv and the turbines by the I. P. Morris 
Co. 

^The three turbine units of the original installation are horizontal 
^.louble units of 6 000 h. p. These are direct connected with single 

• See American Elev trioian. April. !$$«, VoL 10, Xo. 4. 



Plant of the Shawnigan Water Power Co. 



551 




552 



Examplei of Water Power Pla^^ts, 



5,000 h. p* generator units of the rotating field t>"pc, «iih imuSi 
poles. They are designed to operate at 180 r. p. m. ^vii^i 
currents at 30 c^xles per second and 2,200 volts. A Islsr i 



» 




Fig, 339,— Plant of Concord Electric Qi. 
blnes Connected in Taodem. 



S^ V, -aIVs Falls PlanL T«rt!<«l 1 
( Engineer tug Reconi) 



tion consists of two 10,000 h. p. water wheels each driving a6.6o®| 
Ic w. generator. (See Figs. 159 and 236.) 

A separate penstock is provided for the exciter units which COn-| 
sist of two 400 h. p. turbines direct connected to exciters.* 

• See references as given: Eng. Rec. Apr. 2S, 1900; Can. Engr,i Apr. l**!*! 
May, 1901, and May, 1902; El. Wld, and Engr., Feb. 8, 1902: CaMler » MU^ 
June, 1904. 




Plant of the Concord Ekctric Company, 



553 



aSo- Plant of the Concord Electric Company. — This plant, shown 

in Fig, 339, is situated at Sewairs Falls on the Merrimac 

River about four miles from the State House in Concord, New 

Hampshire, The dam is a timber crib- work structure about $00' 

long and gives a fall varying from i6' to I'f, The addition to the 

old plant is the one shown in cross-section by Fig» 339 and is of 

special interest due to the vertical shaft generating units which 

ivere here installed. Comparative estimates showed that all other 

features of the plant, except the machinery could be built cheaper 

ivith the vertical shaft installation and the machinery added only 

a few thousand dollars to the total cost, while other advantages de- 

«rmined its installation. 

The new installation consists of two units, each consisting of 
3 — 55" bronze runners of the Francis type, mounted on a vertical 
shaft and hung on a step bearing. The machines are of the Escher* 
Wyss type built by The Allis Chalmers Company, American rep- 
Tesentatives of the Escher-Wyss Co. The gates are of wicket pat* 
tern, controlled by Escher-Wyss mechanical governors, also built 
l)y The Allis Chalmers Company. The generators, which are direct 
connected to the vertical shaft wheels, are of 500 k, w., 3-phase, 
60 cycle, 2,000 volt, TOO n p. m., revolving field type. Excitation is 
furnished by one 75 h. p., 3-phase, 2,600 volt induction motor, direct 
connected to a 45 k, w., 125 volt, compound wound D. C generator. 
The exciter unit runs at 680 r. p. m»* 

381, Plant of Winnipeg Electric Railway Co. — In Fig. 340 is 
shown the power plant of the Winnipeg Electric Railway Company. 
It is situated on the Winnipeg River at a point a few miles from 
Lac du Bonnet, which is on a branch line of the Canadian Pacific 
Railroad, 65 miles distant from the City of Winnipeg* 

To obtain the necessary water, a canal 120 feet wide and with a 
clear depth of 8 feet at normal low water was cut to the upper river 
near Otter Falls. The canal is 8 miles long, with a drop of 5 feet 
to the mile, equaling a total head of 40 feet. At the point where the 
dam is located there is a natural fall, and the dam crosses almost at 
the crest. 

With the head and discharge available it is claimed that 30,000 
electrical horse power can be developed. 

The water wheels are all McCormick turbines regulated by Lom- 
bard governors. The turbine pits are protected by racks to keep 
out ice, logs, etc, 

• See Engineering Record, Jftnaary 6th, T906L 





Plant of Nevada Power Mining and Milling Co. 



S5S 



electrical units consist of four i,ooo k. w. and five 2,000 k. w. 
ig field, 60 cycle, 2,300 volt, three-phase generators and two 
V. 125 volt, direct-current exciters, all coupled to turbines, 
> 175 k. w. 125 volt direct-current exciters, coupled to three- 
f,300 volt induction motors. 

I are 15 transformers, comprising five banks, by means of 
lie voltage is stepped up from 2,300 to 60,000 volts for trans- 
to the sub-station at Winnipeg over a distance of 65 miles.* 




^i^miiw^*'(^*w^'^^'f"i''' ^ '''' ' ^^" '>' '■■'■'^■^^'■ '^ ^^^■^' ' ^ 



Fig. 341 — Plant of Nevada Power Mining and Milling Co. 
(Engineering Record.), 



^lant of Nevada Power Mining and Milling Co. — Fig. 341 
. section through the plant of The Nevada Power Mining 
ling Company on Bishop Creek, near Bishop, CaL The 
:nt of the station consists of two 750 k. w., 60 cycle, 2,20c 
ee-phase alternating-current generators, running at 450 

and a 1,500 k. w. generator running at 400 r. p. m. This 
inerator is shown in the sectional drawing. There are two 

of 60 k. w. each, delivering current at 140 volts pressure, 
citers are operated by water wheels, and, in addition, one is 
i with an induction motor. The water wheels were made 
Pelton Water Wheel Company of San Francisco. The two 



llectrical World, June 23, 1906. 



556 Examples of Water Power Pbnta. 

750 k. w. machines have Sturgess governors, and die 1,500 k. w. 
machine has a type Q Lombard governor. Hand-cootrol mecfaaO' 
ism is provided for each wheel. Oil is snppfied to die governor bjr 
two oil pumps operated by water wheels. 

Water is taken from the creek at a small diverting dam and can- 
veyed along the moontain-side in a pipe line. The pipe line is aboot 
12^000 feet long, and consists of 6,700 feet of 42-inch wood-stare 
pipe. 2.150 feet of 30-inch wood-stave pipe, and 3,150 feet of 24-iiidi 
steel pipe, all diameters being inside measurements. The 42-indi 
pipe lies on a nearly level grade, the static head at the lower end 
being about 30 feet. At this point are placed two jo-inch gate 
x-alves, one opening into the 30-inch pipe and the other provided for 
a future line. The 30-inch pipe descends the hill to a point that 
gives a static head of 265 feet. Here it joins the 24-inch steel pipe, 
which descends a steep hill to the power house, die total static 
head being 1.068 feet. 

The power generated at the plant is transmitted, over a line (rf 
stranded aluminum, equivalent to No. o copper, to Tonopah and 
Goldfield, Nev., making a total length of line of 113 miles. In 
crossing tlie WTiite Mountains the line reaches ain elevation of over 
TO.500 feet^ 

LirFRATTRR 

1. Hydro-Electric Development at North Mountain. CbL Elea World vA 

Engineer. March 4. 1905. 

2. The Northern California Power Companj's Srstems. Electrical World and 

Engineer. Sept, 10. 1904. 

3. The Power Plants of the Edison Electric Company of L06 Angeles. Eng- 

ineering Record, March IS. 1905. 

4. The Fresno Transmission Plant. The Journal of Electricity, April, 1W€- 

5. The Edison Company's System in Southern California. Electrical World 

and Engineer, March 11, 1905. 

6. An S3-Mile Electric Power Transmission Plant, GaL Caaaier'a Magiiioe, 

November, 1899. 

7. Bishop Creek. Cal. Hydro-Hectrtc Power Plant Electricml World. June 

30, 1906. 

8. The Hydraulic Power Development of the Anim^ Power and Water Com- 

pany. April 14. 1906. Enginering Record. Electrical Reriev. 
Jan. 30. 1904. Engineering News, Jan. 4, 1906, 

9. Power Transmission in Pike*s Peak Region. Electricml World and Ear 

ineer, July 26. 1902. Electrical Worid. Ifay 26, 1906. Engineer 
ing Record. 3klay 19. 1906. Engineering Record. Jnly 19, 1901 



♦ See Engineering Record, June 80, 1906, or Electrical World of June 30. 
1906. 



Literature, 



557 



New Water Power Development at New I^Iilford. Conn. Engineering Rec 
* ord, Feb. 13, 190^, 

ill. Berlishire Power Company, Catiaan, Conn. Eiectrical Review, Sept 7» 1907. 
12. PlEDt of Hartford Electric Light Company, American Electrician, March 
1900. 
lS.Hydrt>-Electric Power Plant and Trauemisslon Lines of the North Georgia 
Electric Company. Electrical Review, Oct. 20. 1906. 
P 14. Atlanta Water and Electric Power Comt>any"s plant at Mor^n Ealla, Ga. 
K Engineering Record, Apr. 23. 1904. 

I IS. Plant of The South Bend Electric Company, South Bend* Ind. ESectricaJ 
^ World and Engineer, May 30. 1903. 

i 18, Plant at Rock Island Arsenal, Rock Island, III. Western Electrician. Nov, 
^ 23* 1901. 

f 11. The Hydraulic Development of the Sterling Hydraulic Company. Engln- 
eering Record, Dec. 16, 1905. 
It. Joliet Water Power of Chicago Drainage Canal. Engineering Record, 

Apr. 19, 1902. 
3$. Development of Electric Power at Shoshone Falls, Idaho. Western Elec- 
trician, Mar. 9, 1907. 

20, Cbandiere Palls Power Transmisalon Company, Maine. Electrical World 
and ESnglneer, June 15, 1901. Engineering News, May 7, 1903. 

21, "Water Power at Portland, Me. Electrical World and Engineer, Jan. 10, 
1903, 

Z2. Plant at Deer Rips, Me. Electrical World and Engineer, Apr. 8, 1905. 
23. Great Northern Paper Company's Kew Mill, Me. Engineering Record, 

Dec. 15, 1900. 

^4, A Submerged Power Station. Md. Engineering Record. Aug. 24, 1907, 
as. High Pressure Power on the Housantonic, Mass. Electrical World and 

Engineer, Feb. 13, 1904. 
26. Development at Turner^s Falls, Mass. 

Aug. 12, 1905. 
27- Power on the Blackstone River, Mass. 

Oct 14, 1905. 
1 3S, New Plant of Holyoke Water Power Company. 

Sept. 15, 190G. 

29, I^whead Hydro- Electric Developments in Michigan. Engineering Record, 

Oct. 19, 1907, 

30. Plant of the Mlchrgan-Lake Superior Power Company, Sault Ste. Marie. 

American Electrician, August, 1S98. Engineering News, Sept, 
25, 1902, Electrical World and Engineer, Nov. g, 1902. 

31. Transmission Plant of Kalamazoo Valley Electric Company, Mich. Am- 

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32, Water Power IJevelopment at Little Falls. Minn., and Its Industrial Re- 

sults. Engineering Record, June 13, 1905. 
SS, SL Anthony Falls Water Power Plant, Minn, American Electrician, Maj 
1S9S. 
34 



Electrical World and Engineer, 
Electrical World and Engineer, 
Engineering Record, 




558 



Examples of Water Power Plants. 



34. Or«&t Northern Power CompaDy of Duluth, Minn. Electrical World. 

July 2S, 1906. 
31. Electric Power TraiiBiiiiBftiQii Plant, Butte, Mont American Hlectrtclas, 

Febraar^i 189$. 
36^ Generating System of Tho Portland General Electric Company. Eneineer 

tng Record* Aug. 12, 190^. 
t7. Tbo Water Power Plant at Hannawa Falls, N* Y, EngiueerlBg Beeorl 

Dec. 7, 1901. 

35. The Water Power Development at Massena, N. Y. Power, December, 1901 
3». HudJion River Power Plant at Mechanic ¥ 111 e, R Y. American U«y 

trlclan, September, ISSS. Engineering News* SepL 1. U^$. Ele^ 
trlcal World, Nov. 13, 1807. 

40. Hudson River Power Plant at Spier Falls, N. Y. Engineering Reoorl 

June 27, 1903. Electrical Review, July 21, 1906. 

41. Hydraulic Developments at Trenton Falls, H. Y. Electrical World, SUf 

19, 1906. 

42. 8 tat ton of Rochester Gaa and Electric Company, Snectrical World tod 

Engineer, Nov. 13, 1903. 

43. Now Hydro-Electric Power Plant of Cornell University. EngineerlBj 

Record, May 20, 1905, 

44. HydrO'Electrlc Developments tn the Adlrondacks. Electrical World, Apr. 

26, 1906. 

45. Hydraulic Development. ^liddletown, N. Y. Electrical World and Ear 

lueer, Aug. 8, 190S. 

4G. Niagara Falls Power Developments. Cassier's Magazine (Niagara f<tnf 
number). Engineering News, 1901, vol. 1, p. 7L 

47- Power Plants of The Portland Railway Light aud Power Company, Port- 
laud, Ore. Engineering News, June 27. 1907. Engineer. Apr. 
15, 1907. 

4S. Qarrln'a Falls Plant, Manchester, N. H. Engineering Record, Jan, !l 

1903. Engineering News^ March 19, 1903. Electrical World i 
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49. Concord, N. H. Water Power. Electrical World and Engineer, July It, Wt~ 

50. Plant at Se wall's Falls, N. H. Engineering Rocord, Jan. 5, 1906. 

61. Water Power at Manchester, N. H. Electrical World and Engineer, jta 

17, 1903, 

62. York Haven, Pa. Tran amission Plant. Electrical World and Engine* 

Sept 19, 1903. Electrical World, March 2, 1907. 

63. Developments at Huntingdon, Pa. Electrical World and KUglneer. 

23, 1906. 

54. Hydro-Electric Plant of the McOall-Ferry Power Company, Fa. Enginet 

Ing Record, Sept. 21, 1907. Electrical Review, June t, 1907, 

55, The Warriors Ridge Hydro-Electric Plant at Huntingdon, Pa. Engtnt* 

Ing Record, Dec. 22, 1906, 
66, Hydro-Electric Developments on the Catawba River, South CaroUfl^ 
Electrical World, May 25, 1907. Engineering Record* July 

1904. Electrical World and Engineer, July 23, 1904, 




Literature 559 

67. Construction of the Neals Shoals Power Plant on Broad River, S. C. Eng- 
ineering Record, March 3, 1906. 

58. A Large Hydraulic Plant at Columbia, S. C. The Engineering Record, 

Jan. 1, 1898. 

59. Greenyille<^rolina Power Company, S. C. Electrical World, June 22, 

1907. 

€0. Water and Electric Power Plant of the Utah Sugar Company. Engineer- 
ing News, Apr. 13, 1905. 

€1. Bear River Power Plant and Utah Transmission Systems. Electrical 
World and Ehgineer, June 18, 1894. 

42. Plant of the Chittenden Power Company, Rutland, Vt Engineering Rec- 
ord, Dec. 9, 1905. 

€3. Plant of Vermont Marble Company, Proctor, Vt Electrical World, Feb. 

3, 1906. 
^. Water Wheel Equipment in the Puget Sound Power Company's Plant. 

Electrical World and Engineer, Oct. 22, 1904. 

^. Hydraulic Power Plant on the Puyallup River, near Tacoma. Engineer 
lug Record, Oct. 1, 1904. Engineering News, Sept 29, 1904. 
Electrical World and Engineer, Oct 1, 1904. 

^6. Snoqualmie Falls Water Power Plant and Transmission System. Eng- 
ineering News, Dec. 13, 1900. Western Electrician, Aug. 20, 1898. 
Electrical World and E^ngineer, May 7, 1904. 

^7. Apple River Power Plant, Wisconsin. Electrical World and Engineer, 
Dec 8. 1900. 

^^ 8t Croix Power Company, Wisconsin. American Institute of Electrical 
Engineers, 1900. Engineering Record, March 3, 1906. Western 
Electrician, Oct 27, 1906. 

«. The Lachine Rapids Power Plant Montreal, P. Q. Engineering News, 
Feb. 18, 1897. 

*^0. Shawinigan Falls Electrical Development Electrical World and Eng- 
ineer, Feb. 1, 1902. Cassier's Magazine, June, 1904. Engineer- 
ing Record, April 28, 1900. Canadian Engineer, April and May, 
1901 and May, 1902. 

^L 60,00a-volt Hydro-Electric Plant Winnipeg. Manitoba. Electrical World, 
June 23, 1906. 

^1 DeCew Falls Power Plant Engineer, Apr. 2, 1906. 

"^ Development of the Montmorency Falls. Electrical World and Engineer, 
June 17, 1899. 

"^i The Rheinfelder Power Transmission. Electrician, March 26, 1897. 

"^5. The Bellinzona, Italy, Hydro-Electric Station. Electrical World and Eng- 
ineer, Sept 16, 1905. 
n^i A Norwegian Water Power Plant Electrical World and Engineer, Apr. 

4, 1903. 

^. An Italian 40,000-volt Transmission Plant Electrical World and Eng- 
ineer, Aug. 19, 1905. 
^ Tyrol Hydro-Electric Power Station, Keiserwerke. EZlectrical World, May 
1. 1907. 



- : :i3f 



CHAPTER XXIII. 

rHE RELATION OF DAM AND POWER STATION. 

I3. General Consideration. — In any water power plant the 
IT must be taken from some source, conducted to the wheels, 
discharged from the same at the lower head. To accomplish 
object there must be a head-race leading from the source of 
)ly to the plant which may be of greater or less length and in 
:h more or less of the available head may be lost in order to 
luce the velocity of flow and overcome the frictional resistance. 



Pig. 342. 

iter entering the plant the water is discharged through the 
>ine T into a tail-race of greater or less extent in which there 
Iso a loss caused by friction and velocity of flow, similar to that 
ady expended in the head-race. In Fig. 342 the total head 
tlable is H ; the head lost in the head-race is indicated by hj ; 
the head lost in the tail-race is indicated by hj. The net energy 
lie wheel is h = H — hj — hj, and a portion of h is also lost in 
slip, leakage, and friction of the machinery and transmission* 
Tie power plant should be located with reference to the dam* 
liat (i) the greatest amount of head may be utilized at the least 
«nse; (2) the plant constructed should be as free as possible 
H interruptions due to floods or other contingencies; (3) the 
ition chosen should be at such' a point where security of con- 
tction can be accomplished at the minimum expense. 
-ach of these influences is of importance and the relative location 
tlie power plant and dam must depend upon these and various 
er conditions which must be carefully considered. 



56a The Relation of Dam and Power Station. ■ 

284. Classification of Types of Development, — For the pufpOH 

of a dear understanding of the principles invoh^ed, the type ■ 
development may be grouped or classified into : ■ 

First: Concentrated fall, in which the plant is built on tbedifl 
or closely adjoining thereto, with a short or no race. In this cafl 
the entire fall is concentrated by means of the dam and as a nfl 
this class of development is adaptable only to central power ?l^ 
tions where one or two plants only are to be installed oa M\ 
power. ■ 

Second: Diversion type with dam. In this case the fall is M 
vcloped by means of a dam in the manner conforming to tiic lifl 
type but the water is distributed to one or more plants by meaafl 
of a long head-race canal throug^h which the water flows to tk 
power station, after which it is discharged either into the stream 
at some point below the dam or into a tail-race from which it is 
finally discharged at a point lower dowTi the stream. 

Third: Diversion with or without dam. In this case the develop* 
ment is installed with or without a dam at the head of the rapids 
or fall which is to be utilized and the water is conducted througfi 
a long head race, if land of a suitable elevation is available, or*, 
otherwise, through a tunnel to a point immediately above the site 
of the power station. From the end of the tail-race or tunnel tf^e 
water is carried to the plant through a metallic penstock. 

Fourth : The fourth type is similar to the third except that where 
the head-race or tunnel is used (the ground being unfavorable tp 
such construction or the expense of the same being unwarranted) 
a long penstock of metal is provided to conduct the water horn 
the head works to the station. 

Fifth : The fifth type is the tunnel tail-race type and involves con- 
ducting the water through metallic penstock direct to the wheels 
located at the minimum level and, after the water is dlschargtd 
therefrom, the provison of a tunnel tail-race for conducting the 
water from the turbine to the point where it is to be discharged 
back into the stream- 
It is important to note in this case, as in the case of all other 
classifications attempted, that such a classification is for the pur- 
pose of systematizing the consideration of numerous diverslfiecl 
types and bringing them to a similar basis for examination* In 
the actual adaptation of plans of development, it is seldom any sin-j 
gle type will be found in its simplicity; in most cases modifications'* 
of the same become desirable or essentiaL 




m m 



Classification of Types of Development. 



56s 




5^4 The Relgtioo of Dam and Power 

285. Concentrated FalL^ — ^lo most of Cbe low bead wmter powers 
ihe portioci of the fall of tlie river which can be txtlfized is d^tiib- 
tited over minor rapids and small falls and occttpies m coosidcfable 
length of the stream. Where the head is small and the expense of 
m dam to eoncentrate the head entirely at one point is permissibirp 
the power house may sometimes be located to advmntage tn tiie dm 
itse'tf. In this case the power bonse will constitme a part of tk 
dam itself. This is possible only where the lepgth of the spillway 
remaining is sufficient to pass maximum flood without an undue 
rise in the head of the water above the dam* lit many stich cases 
this plan, which is represented by Diagram C Fig. 343, mefti 
economical construction as it may both cheapen tke cost of the 
dam and reduce the excavation nec^^ary for the wheel pit and t2il> 
race. The power house built at such point is* however, usmllv 
directly in the line of the current and must be so constructed w^ 
protected as to prevent its injury or destnsctioo by floods^ ice or 
other conting^encies of river flow. 

In other cases, where the spillway available by the above plan is 
not sufhcient or where the plant is not properly protected b]r such 
forms of constniction, the plant may be constructed on one side 
of the dam, receiving its waters from a head-race which jom thf 
river above the dam and discharges it into the river below, ^ 
shown by Diagrams C and D, Fig, 343. Or, where the capacity i* 
si^tablep the plant itself may receive the water directly from sl^ 
head gate from the river above the dam and discharge it through 
a tail-race which will enter the river at some point below the dam. 
as shown in Diagram A» Fig. 343. 

In other cases, where the power is to be distributed to a number 
of independent plants, raceways may be constructed on either of 
both sides of the stream and from the dam, following the stream 
downward along the bank and more or less approximately parallel 
thereto as the nature of the conditions demand The plant drawing 
the water from this head-race may be distrbtited at various pomi^ 
along the same, and from these plants the water will be discharged 
after use either directly into the stream itself or into a tail race con- 
necting such plants with a lower point farther down the streajHi** 
shown in Diagram E, Fig, 343, 

a86. Divided FalL — An independent tail-race is usually coi^- 
structed to advantage where the dam concentrates only a portioci « 
the head or fall, leaving certain additional portions to be develop 
by the use of the tail-race, which may, if desirable, enter the strewti 




Classification of Types o£ Development 565 




566 The Relation of Dam and Power Station. I 

at a point much tartlier down the ri%^er and at the foot of the rapiB 
Where the fall of the stream is considerable, and the expensed 
construction of the dam to suitable height to concentrate Uie entfl 
fall at a single point is inadvisable, it is often desirable to btiilM 
dam to less height at perhaps considerably less expense and devdn 
at the dam only a portion of the total fall From this dam a heafl 
race may extend to some considerable distance, and the ^vaterfral 
this head-race may be delivered to the power plant a mile or t<rl 
lower down the stream. From this head race, the water, after pa<? 
ing throw gli the wheels, is carried directly into the stream at tie 
lower point, as shown in Diagram G, Fig. 344. 

Under other conditions, where the topography of the country is 
suitable, the head-race may be much less in extent, and a tail-race 
substituted for receiving the waters after they have been usd ifl 
the wheel and then conducted to the river at or near the ^nd of tk 
rapids, as shown in Diagram F, Fig. 344. 

Under still other conditions the plant itself may be located Immt- 
diately at the dam and the tail waters may be conducted from the 
turbine to a tail-race or tail-water tunne! to the lower end of the 
rapids, as in Diagram H, Fig, 344. 

The relation of head-race and tail-race is merely a question d 
developing the power plant at the least cost and securing the max- 
imum head, and the topographical conditions at the power site will 
therefore determine which line of development will be best. In a 
number of cases, where the head or fall ip considerable and thf 
power development is large, and where the cost of land for head- 
races w^ould be almost or quite prohibitive, the stations have b«Ji 
located in the immediate vicinity of the river and have delivered the 
water into a tail-race tunnel, which frequently empties at a coo- 
siderable distance down the stream and at the lowest point of deliv- 
ery that is practicable. In other cases it is more economical tonin 
open raceways for a portion of the distance and then conduct the 
water under pressure by closed pipes to the wheels at the lower 
point. 

This last method is used particularly under high head and where 
the water must be conducted for a reasonable distance over an irreg- 
ular profile. 

The quantity of water to be used, the head available, and the 
value of power modify the arrangements which must be carefully 
studied in view of the financial, topographical, and otheT modifyin| 
conditions. 




J 



Distribution of Water at Various Plants. 



567 



287. Examples of the Distribution of Water at Various Plants. — 
ig. 345 is a plan of the power development on the Rock River at 
:erling, Illinois, The dam at this point is about 940 feet in length. 
he power is owned by various corporations and private individuals 
ho have combined their interests in the dam and raceways and 




345.— Raceways of Sterling Hydraulic Company. 



wve organized The Sterling Hydraulic Company, whose function 
s to maintain the same. The individual plants are owned, installed, 
ind operated by the various owners or by manufacturers who lease 
he power. At this location races have been constructed at the foot 
>f the rapids, but these rapids continue to a point near the lower 
nd of the tail-race, and the plants farthest from the dam have the 
ighcst falls. The fall varies from abooit 8 to 91^ feet 



568 



The Relation of Dam and Power Station. 



Tig. 346 shows the general arrangement of the canal of The Hoi* 
yoke Water Power Company at Holyoke, Mass* The total fall d 
the river at this point, from the head water above the dam to t!ir 
tail water at the loivvest point down the stream, is about sixty feci 
The fall is divided into three levels by the variotis canals, martd: 
ist level canal t 2nd level canal, and 3rd level canal. 




Fig. 3-4lj.^Caaals of Holyoke Water Power Compimy. 

The first level canal, which has a length of about 6,ooa feet, {5c»:ju* 
structed as a chord across the bend of the river and is approximatd|j 
some 3,000 feet from the bend. The canal is about i^c^ wide near^ 
the bulkhead and decreases to about loo' at the lower end, Tbe 
water depth is about 20' at the upper end and about lo' at the bwtr* 
The canals are all walled throughout their length to a height twoorj 
three feet above the maximum water surface. The fall from M 
first level to the second is about 20', Various mills draw^ their watfrj 
supply from the first level as a head-race, and discharge into the 
second cana! as a tail-race. Near the upper end of the canal ar^* 
few factories that draw water from the first level and dischargcil^*| 
same into the river with a head of some 35 or 40 feet 

The second level canal is built parallel to the first and at a &r\ 
tance of about 400 feet nearer the riv^er. The main canal is about 
6,500 feet in length, but near the left hand of the map is shown toj 



Distribution of Water at Various Plants. 



569 




Fig. 347. — 'Kilboum Plant of Southern Wi8con«ln Power Co. 



570 



The Reiatioo of Dam and Power Station* 



sweep round towards the river and attain a reach of about 3,005 
feet in length parallel thereto. The mills drawing their supply frous 
this canal discharge either directly into the third level or into tlie 
river. The water supply frotn each of the lower levels is the tail 
water from the next level above, but is also supplemented by over- 
flows wheti the mills fed from the level above are not discharginf 




Fig, 348. — Plant of The Lake Superior Power Cq» 

sufficient water to maintain the quantity needed in the lower levd. 

The fall from the third level of the river is essentially the sanat 
for all the mills drawing water therefrom, but according to the stag? 
of the river ranges from 15 to 27 feet. 

The flow of water in the first level is controlled by gates and its 
height limited by an overflow of about 200 feet in length whkB 
acts as a safety overflow and prevents any great rise in the hm 
water during times of flood. 

fl88* Head-Races Only. — Fig* 347 illustrates the general plan of 
the hydraulic power development of The Southern Wisconsin P<>wef 
Company at Kilbourn^ Wisconsin, Here the entire cross-section of 
the stream is necessary in order to pass the maximum volume of 



Distribution of Water at Various Plants. 



571 




a 

o 



I 



o 



I 



^ 

^ 



Distribution of Water at Various Plants. 



573 



water, which amounts to about 80,000 second-feet The plant has 
therefore been constructed at one side of the river, receives the flow 
through a series of gates built just above the dam, and discharges 
the water into the river just below the bend in the river, as shown. 
The plant now under construction is only a portion of that which 
it is designed to ultimately install. The proposed future extension 
of the power plant is shown by the dotted lines. 



/P -*^^^^-"^ ^ 



^j^ ^"- 



TWIM FMAi 




F1?. 351. — Possible Canal for Peshtlgo River Development 

Fig. 348 shows the water power plant of The Lake Superior 
I^owcr Company at St. Mary's Falls, Michigan. The canal on the 
American side begins just above the entrance to the American ship 
c^anal and above the Soo rapids. The water is cond^ucted through 
this canal to a power house located below the rapids at the point 
shown on the map. On account of the value of the land this canal 
"Vas designed for a velocity of flow of about 714' per second with 
*ull load of the plant, which was designed for about 40,000 h. p. 
JPcquiring a capacity with available head of 16.2 feet, of about 4,200 
^^bic feet ner second. (See Engineering News of August 4th, i8g8.) 
36 



574 



Tne R.-^aroii at Dam sad Power Statioa. 



F!g: 345 rioiws -iie alaa at zhe aydrxsEc development of The 
Ecrinamy Lighr and Power Gmpaznr at JoIiMt, Illinois. The entire 
installatiaii 3S ^cwn is owned by dtfs companr. The fall available 
is about ix fiest and is dcTeioped by a concre t e dam which creates 
the up per basin alon^ wrrrrh die power plant has been constructed 
The water f ows rfiron^ the finmc gates directly on to the wheels 
and is discharged iatD a tail-race bnxlt parallel with the river A 





! 




k 






t 
s 


u 








tM 




( 








840 












tM 




\ i 






SIO 




/ 








...s 


1 


— -— — 'T^ i 








800 


z 


' ! 1 








790 


YZ 


! \ 








7tO 


) 


i 










770 


i 


1 










m 



60 



61 



60 



64 



66 



MIUBS 

Fig. 352.— Profile of Peshtigo River. 



certain amount of water is necessary for feeding the lower level of 
the canal and this is supplied by a by-pass tunnel shown in dottco 
line above the dam. This by-pass, which is slightly higher than 
the elevation of the tail-race, is fed by the discharge of one of the 
wheels, which operates under a less head than the other wheels ifl 
the installation. 

289. Plant Located in Dam.— In Fig. 350 is shown the general 
plan and elevation of the hydraulic plant at Dresden Heights 00 the 
Des Plaines River just above its junction with the Kankakee Ri^^^- 
1 licse two streams unite at this point to form the Illinois River. 

In this case the dam is built across a very wide valley and the 
length of the dam is much greater than necessary or desirable to 



High Head Developments 



575 



i 



o 

I 



& 

a 
o 

•4-* 

a 

0) 

u 

a 
B 

O 

•33 

► 

Q 

u 

9 




accommodate the flood flow of the 
stream which is approximately 25,000 
second-feet. In consequence, the pres- 
ent power plant, as well as the pro- 
posed extension to the power station^ 
will form a part of the dam itself and 
the spillway will occupy only a portion 
of the entire length of the structure 
and is so designed as to maintain a sat- 
isfactory head at times of flood flow 
The head of the water above the dam 
is controlled both by the length of 
spillway and by six tainter gates by 
means of which the level of the water 
above the dam can be controlled at all 
stages of flow. 

290. High Head Developments. — 
Fig. 351 illustrates the general plan of 
a possible method of development of 
the Peshtigo River for The Northern 
Hydro-Electric Company. The fall 
available is shown by the profile, — Fig. 
352. It is proposed to construct a dam 
above High Falls of sufficient height 
to back the water over Twin Falls^ and 
to either develop the power at High 
Falls and Johnson's Falls independently 
or conduct the water by a canal to Mud 
Lake, thence to Perch Lake, thence to 
the head work to be be built above 
Johnson's Falls, where a head of about 
110' will be available. If a single de- 
velopment is chosen the water will be 
be conducted from the head works 
through penstocks to the power plant 
to be built at the base of the bluff below 
Johnson's Falls. The canal in this case 
will conduct the head waters with very 
little fall to the immediate site of the 
plant, thence by penstocks to the tur 
bine located in the gorge below. 



and Power Station. 




Fig* ^&4---Niagara Falls Fower Dev«i»piiieiii* 





Hi^h Head Developments. 



577 



^^E' 353 *s a plant of the power devclcpment at Trenton FalJs, 
^^ew York. The upper portion of the fall is developed by a dam 
ibout 60^ in height, which is connected by an 84" pipe line with the 
tirbiTie located in the power house about two miles below. The 
^urbines used in this development are the Fourneyron turbines, 
^^wrhich are described in Chap, XIX, and are illustrated by Fig. 311, 

Fig. 354 is a general plan of the water power de%^etopments at 
^^iagara Falls, The first development was that of The Niagara 






Falls Hydraulic and Manufacturing Company. By means of a 
canal the water is taken from the upper end of the rapids and con- 
ducted to the lower bkiff on the American side, and distributed, by 
open canals, to various plants located along this bluff.. 

Ttie second plant constructed was that of The Niagara Falls 
Power Company; in which power is developed by the %^ertical shafts 
connecting with a tail-water tunnel %vhich discharges into the river 
just below the new suspension bridge* 




578 The Relation of Dam and Power Station. 

On the Canadian side are shown three plants. 

The Ontario Power Company secures its water supply from the 
upper portion of the rapids, conducting it through steel conduits 
to a pc«nt above the power house and thence by penstocks to the 
wheel, located in the gorge below the falls. 

In the plants of The Toronto and Niagara Power Company md 
The Canadian-Niagara Power Company, the water is taken from 
above the Falls and discharges through penstocks to wheels looted 
at the base of a shaft and thence into tunnels, discharging intofte 
river at a point below the Falls. 

Fig. 355 illustrates the plant of The Niagara Falls Hydraulic tod 
Manufacturing Company, which is supplied by water from Ae 
hydraulic canal above mentioned. The water is conducted from fte 
forebay by a vertical penstock to which is attached several wheels 
which deliver the water into a tail-race tunnel and thence into Ae 
gorge below. 

The plant arrangements ab©ve described are typical of many not 
in use both in this country and in Europe. It is at once obvious ttat 
in considering this subject each particular location is a problem by 
itself which must be considered in all its bearings; but an under- 
standing of the designs and arrangements already in use forms t 
satisfactory basis from which a judicious selection can be made 
with suitable modifications to take care of all the conditions of 
topography and other controlling conditions. 



CHAPTER XXIV* 
PRINCIPLES OF CONSTRUCTION OF DAMS. 



agi. Object of Construction. — A dam is a structure constructed 
with the object of holding back or obstructing the flow and elevat- 
ing the surface of water. Such structures may be built for the fol- 
lowing purposes : 

First: To concentrate the fall of a stream so as to admit of the 
economical development of powen 

Second : To deepen the water of a stream so as to facilitate nav- 
igation and to so concentrate the fall that vessels may be safely 
raised from a lower to an upper level by means of locks. 

Third: To impound or store water so that it may be utilized as 
desired for water supply, water power, navigation, irrigation, or 
other uses. 

Fourth: In the form of mine dams or bulk heads to hold back 
the fiow of water which would otherwise flood mines or shafts or 
cause excessive expense for its removal. 

Fifth : As coiTer-dams for the purpose of making accessible, 
usually for construction purposes, submerged areas othervvise inac- 
cessible. 

39a* Dams for Water Power Purposes. — The primary object of 
a dam constructed for water power purposes is to concentrate the 
fall of the stream so that it can be developed to advantage at one 
point and so that the water thus raised can more readily be delivered 
to the motors through raceways and penstocks of reasonable length. 
This object is sometimes accomplished in rivers with steep slopes 
or high velocities by the construction of wing dams which occupy 
*only a portion of the cross-section of the stream, but cause a head- 
ing up of the water and direct a certain portion of the flow into 
the channel or raceway through which it flows to the wheels. 
Usually in streams of moderate slope the dam must extend entirely 
across the stream in order to concentrate sufticient head to be of 
practical titility. 




£3o Trindpies of Coostractkn of Dams. 

\\':r.^ dzzr.s can be used at the head of high tails where onlv a 
portior^ of the volunie of flow can be utilized, as at Niagara Falls, 
or in rapid rivers where a portion of the flow is to be directed into 
a narrow channel for txtilizing low heads by means of midershot or 
•!oat wheels as is frequently done for irrigation purposes. Where 
the full benefit of both head and volume is to be utilized the dam 
must extend from bank to bank and be constructed of as great a 
height as possible. 

293. Heig^ of DaoL — ^To utilize a river to the maximnm extent 
the highest dam practicable must be constructed. 

The height of a dam may be limited by the following factors: 

First : The overflow of valuable lands. 

Second: The interference with water power rights above the 
point of development. 

Third : The interference with other vested or public rights. 

Fourth : The cost of the structure. 

The value of the power that can be developed by means of a pro- 
posed dam will limit the amount that can be expended in the pur- 
chase or condemnation of property affected by backwater from the 
dam and the cost of its construction. These are among the cl^ 
ments of the cost of the project and must be considered together 
with other financial elements before a water power project can be 
considered practicable. 

In considering backwater and its effect on riparian rights both 
high and moderate conditions of flow must be considered. The 
former condition gives rise to temporary interference, often of little 
importance when affecting purely farming property, and the real 
or fancied damages from which can commonly be liquidated by re- 
leases at small expense. The latter conditicwi will permanently 
inundate certain low lands which must be secured by purchase or 
condemnation. In many states where the laws of eminent domain 
do not apply to the condemnation of property for such purposes it 
is necessary to secure such property by private purchases before 
the work is undertaken, and usually before the project becomes 
known publicly, for in such cases the owner of a single piece of land 
may delay the project by a demand for exorbitant remuneration, 
from which demand there is in such cases no escape- In every case 
it is desirable that riparian and property rights be fully covered 
before the construction of the project actually begins. 



The Foundalion of Dams. 581 

294. Available Head* — Beside the question of backwater the ques- 
tion of head at the dam is important both in relation to the question 
of interference and in relation to the question of power. In relation 
to interference it is an easy matter with a known length and height 
of dam to determine by calcalation from a properly selected weir 
formula the height of water above the dam under any condition of 
flow. To determine the head available under all conditions of flow 
the weir cur\^e must be studied in connection with the rating curve 
as discussed in Chapter V. 

Two conditions of flow often require consideration in this con- 
nection : 

First: Where a considerable portion of the flow is being utilized 
by the wheels and therefore does not aifect the head of the dam* 

Second: Where the water is not being used by the wheels and 
consequently aflfects the head of the dam. 

Both of these conditions should be studied and determined in rela- 
tion to their influence on both backwater conditions and power. 

295, The Principles of Construe tian of Dams, — The general prin- 
ciples for the construction of all dams are similar, and are as fol- 
lows : 

First : They must have suitable foundations to sustain the pres- * 
sore transmitted through them, which must be cither impervious or 
rendered practically so. 

Second: They must be Stable against overturning. 

Third: They must be safe against sliding. 

Fourth: They must have a sufficient strength to withstand the 
strains and shocks to which they arc subjected- 

Fifth : They must be practically water-tight. 

Sixth: They must have essentially water-tight connections with 
their beds and banks* and, if bed or banks arc pervious, with some 
impervious stratum below the bed and within the banks of the 
stream. 

Seventh: They must be so constructed as to prevent injurious 
scouring of the bed and banks below them. 

The application of the ab(ive principles depends on the material 
from which the dam is to be built and on local conditions- 

396. The Foundation o! Dams. — The materials used for the eon- 
struction of dams may be masonry, which includes stone-work and 
concrete-work, reinforced concrete, timber, steel, loose rock, and 
earth. Each may he used independently or in combination. 
Masonry and concrete dams must be built upon foundations which 



55*3 



PfVtC^llcS' oc 



are p racticall y free frooi possHife setticEneiii:. SataH masoory siiac- 



torn ntxf soinetiincs be saMj eoBStractcd cw piles or piUi^ 
bsaed on flofter ntatemis ; bnt tbe lafger and more tm- 
ilfiscliuesip if coostmcted of sBsoorf* oa be safely buiU 
only tipofi solid rock. Ressforced coocrefe is now betn^ exteosheh 
osed for small structtires and is not as sctioosl y affected by sUgiit 
s^Uemeat as in tlie case o( dams ct sofid masoeiy. There is, hew- 
ever, little fle^dbility in structures of this kind, and die foniKlition 



^ 



I I 



^ K^i. 



-"^ 



V^ 



Fif. 356,— Timber (Mb Dmm mi JkntrnwUlt* Wis. 

must be selected in accordance with this fact. Timber and steel 
possess a flexibility not possible in concrete construction and ire 
much better adapted to locations where the foundation may be sob- 
jcct to settlement. 

In construction on rock foundation it is usually desirable to exca- 
%'ate trenches therein in order to give a bond between the stniciure 
of the dam and its foundation. It is also essential with rock foun- 
dations to determine whether cracks or fissures in the foundation 
extend below the structure, and if such are found, they must be 
completely cut off, « 

On earth, sand or gravel foundations, when such must be ti^» 
the flow which would take place through these materials and nni^f 
the structure of the dam must be completely cut off by the use of 
steel or timbi^r sheet piling* which, if possible, should be driven 
from the structure to the rock or to some other impervious strattsm. 
If no impervious stratum is accessible, the sheet piling must he 



k. 



Strength o£ Dams. 



58j 



ren to stich a distance below the base of the dam that the friction 
of the flow of water nnder it will reduce or destroy the head and 
consequently reduce the flow of water to an inappreciable quantity, 
297. Strength of Dams.^ — A dam to be built in a flowing stream 
should be designed with a full appreciation of all the stresses to 
which it may be subjected* Of these, stresses that are due to static 
pressure can be readily estimated from the known conditions. The 
strains due to dynamic forces are not so fully understood or easily 




Fig. 3->7.— Janes vj lie Dam with Mcderate Watcn 

calculated. Where the structure is constructed to retain a definite 
head of water without overflow, as in the case of reservoir embank- 
ments, the problem becomes one largely of statics and the only 
other stresses to be considered are those due to ice action and the 
action of waves on the structure. When a dam is constructed in a 
running stream and is subject to the passage of extensive floods of 
water over it, frequently accompanied by large masses of floating- 
ice, logs or other material which in many cases may strike the 
crest of the dam, and bring unknown and violent strains, the prob- 
lem becomes largely one of experience ?.nd judgment. 

298, Flood Flows. — The passage of great volumes of water over 
a dam involves the expenditure of the power so generated upon or 
immediately adjoining the structure, and unless preparations are 
made for properly taking care of this immense expenditure of 
power, the power may be exerted in the destruction of the structure 
itself. 





584 



Principles of Const rucliDEi o£ Dams, 



f^igs. 356 to 358 show three views of the timber crib dam 

Janesville, Wisconsin, under various conditions of flow. In Fi§* 
356 the flow of the river is comparatively small and all of the water 
is bcin^ used in the power plant, none passing over the dam. In 
Fig, 357 the river is at a moderate stage and the greater part of the 
(low is passing over the crest of the dam. In Fig. 358 some four 
or five feet of water is passing over the dam and the power tliat h 
developed thereby is causing the standing wave and the roup 




Fig. 358,^Jftne8vine Dam under HtgU Water. 



water shown in the picture below the dam. At this point the power 
developed by the fall is being expended in waves and eddies, whidu 
unless properly controlled, will attack and injure or destroy the 
structure. On rock bottom the rock itself will sustain the impact of 
flow over small dams. But where the rock is soft, or the bottom is 
composed of material that can be readily disintegrated, it becomes 
necessary to extend the structure of the dam itself in the form of 
an apron to cover and protect the bottom. 

Fig, 359 shows the preliminary design of a dam for the SontTiern 
AVisconsin Power Company, now under construction at Kilbourn. 
Wisconsin^ This dam will be about 17 feet in height above low 
water and will be subject at times to the passage of floods to a 
depth of 16 feet above its crest. For section of dam as constructed 
see Fig, 373, The two ends of the dam will rest upon a rock 
foundation. Cribs are also carried to the rock at the face of the 
dim and at the edge of the apron. The center of the dam is stis- 



I 





586 Principles of Construction of Dams. 

tained by piles reaching to rock but surrounded by sand which is 
retained by the cribs. 

The dam proper is built of cells 6 feet squarCp the walls of eadi 
<reli being built of solid timber, and each cell carefully filled with 
stone and sand. At the face of the dam and at the toe of the aproa 
triple sheeting has been placed and sscurely fastened to the 4mi 
and cribs from the rock up, thus eflfectively preventing the passage 
of water below or through the dam. 

During high floods the amount of power which must be wasted ib 
the passage of water over the dam will exceed 100,000 horse powtr 
In order to prevent the expenditure of this power in the destruction 
of the dam, the dam is extended in an apron of about lOO feet in 
width, the total wfdth of the structure including the dam and the 
apron, being about 150 feet. 

To further protect the structure, rip-rap is deposited both above 
and below the structure itself. The surface of the dam exposed at 
times of low water is constructed of re-inforced concrete, attached 
directly to the timber work of steel reinforcement* By this design 
a structure is obtained having all the advantages of the flexibility nf 
timber, with the lasting qualities of masonry, for the concrete only 
will be exposed at times of low w^ater, all timber work being sub- 
merged under every ordinary condition. 

299. Impervious Construction- — Masonry dams are commonljf^ 
made impervious by the structure of the masonry itself. ■ 

In timber crib dams ordinarily no attempt is made to make the 
structure itself water- tight, but the top and upstream side are usu- 
ally covered with water-tight sheeting to prevent the water pass- 
ing into and through the cribs* Such water as reaches the timber 
cribs usually passes away readily through the open structure on thc^ 
down stream side of the dam. ■ 

In the construction of rock-filled dams the same condition ordi* 
narily obtains. The dam is fairly porous with the exception of its 
upper face which is made practically water-tight by the use of con- 
crete, puddle, or some impervious paving. 

In earthen dams the finer and more water-tight materials are 
used on the inner slopes of the embankment, and, in addition 
thereto, it is customary in large and important works to use a corf 
of concrete or puddle to effectively prevent the passage of water 
through the structure* 

300* The Stability of Masonry Dams. — The external forces act- 
ing on a masonry dam are the water pressure, the weight of iht 





Stability of Masonry Dams. 587 

masonry, the reaction of the foundation, ice and wave pressure near 
the top, wind pressure, and back pressure of the water 00 the down 
stream side. The action of these forces may cause a dam to faU by : 
(i) Sliding on the base or on any horizontal plane abonre the 
base. 

(2) Overturning. 

(3) Crushing the masonry or foundation. 

If the dam be built of rubble masonry there will be no danger of 
failure by sliding on a horizontal joint above the foundation and 
experience has shown that where a good quality of mortar is used 
it can be depended upon to prevent sliding in concrete and stone 
dams having horizontal bed joints. The joint between the dam and 
its foundation is a more critical point In rock foundation steps or 
trenches should be cut so as to afford good anchorage for the dam. 
In the case of clay, timber or similar foundations the dam will have 
to be made massive enough so that the tangent of the angle be- 
tween the resultant pressure on the base and a vertical line is less 
than the co-efficient of friction between the materials of the dam 
and the foundation. 

It is customary in the design of masonry dams to proportion the 
section so that the lines of resultant pressure at all horizontal 
joints, for both the conditions of reservoir full and reservoir 
empty, shall pass through the middle third points of the joints. 
If this condition is fulfilled, the factor of safety against overturn- 
ing at every joint will be 2, and there will also be no danger from 
tensile stresses developing in the faces of the dam. 

Investigation has shown that there is no danger of crushing the 
masonry except in very high dams, with the consideration of which 
we are not here concerned- 

301. Calculation for Stability. — ^The general conclusion may there" 
fore be stated, that, in the case of ordinary masonry and con- 
crete dams, not over 100 feet in height, to be built on rock foun- 
dations, the design can be based upon the condition that the lines 
of pressure must lie within the middle third of the profile 
This rule must be modified at the top of the dam to resist the 
stresses due to waves, ice, etc. The force exerted by ice is an in- 
determinate quantity and the tops of dams must therefore be pro- 
portioned in accordance with empirical rules. Dams are built with 
top widths varying from 2 to 22 feet, the broader ones usually 



588 



Principles of Construction of Dams. 



carrying a roadway. Coventry suggests the following empirical 
rules for width of top and height of top above water level* 

(1) b = 4.0 + 0.07 H 

(2) y, = 1.8 + 0.05 H 

Where b is the width of top, y© the height above water level and 
H the greatest depth of water. Both faces of the dam will be ver- 
tical until the depth vi, is reached, where the resultant force passes 
through the middle third point. Below this depth the general nilc 
will apply. In computing the water pressure against the dam, it 




Fig. 360. 

is best to consider the water surface level with the top of the dam 
in order to allow for possible rises due to floods, etc. Having de- 
termined the top width, b, and assuming a section of the dam one 
foot long, the height, y^ of the rectangular portion can be deduced 
from the formula 

(3) y, = hVr 

in which s is the specific gravity of the material of the dam. 

The down-stream face of the dam must now be sloped so as to 
keep the resultant pressure, with the reservoir full, at the Hmit of 
the middle third of the length of any joint. Dividing the remainder 
of the height of the dam into lengths convenient for computation, 
the IciiL^th of any joint, (see Fig. 360) as "GH may be found by the 
formula 



Calculation for Stability, 589 



rhich 



em(ATeftABFE) BH» , 

FH 1 FH ^*^ 

frliere m = distance from F of the line o£ action of the weie^t of 
tDasonr>^ above EF and 

r4 (Areit ABFE) 



=i[i^^^5^UKF] 



rhc value of n is given by the equation 

Mom. of ABFE + Mom. ©f EFHO 



(5) 



(AreaABHG) 



moments being taken about the point H, 

Equation (4) can be used as long as n is greater than one-third 
the length of the joint When this condition can no longer be sat- 
isfied with a vertical face, it will be necessary to batter the upstream 
face also^ so that the lines of pressure with reserv^oir full and empty 
both lie at the limits of the middle third of the length of any joint. 

The length of the joints, as IJ, may now be found by the formula 



I 



• ,fl\ TT ^rSK" , /(TTT . (AreaABHG) \ (Aw« ABHG) "gR 

and the value of KJ, is 

— 2 (AreaABHG) (TJ — l^m) — fHK X 55"*) 
^ ' " 6 (Area ABHG) +irK C2GH + IJ) 

In high dams two more stages, governed by the compresstve 
strength of the masonr>% would have to be considered, but, within 
the limit of height set above, the formulas given are sufficient 

The position of the line of pressure may be readily determined 
also by graphical methods. 

In the case of overfall dams, which are necessarily subjected to 
dynamic forces, which are more or less indeterminate, the design 
cannot be so closely figured. 

302. Further Considerations.— The preceding analysis does not 
take into account the possibility of an upward pressure from below 
the dam, due to the previous character of the foundation, or to 
cracks and fissures, by means of which the pressure of the head 
water may be transmitted to the base of the dam. This factor is 
_commonly ignored in dam construction, but should be considered. 




59» 



PriiKiples of Constructioii of Dama. 




ilf^ Ul, 



Uon of Dam of Hdlroke Wat«r Power 0^ 




Fig. 3S2.— liraMary Dam of Holyoke Water Power 



Further Considerations, 



591 



ind, when occasion requires, the foundation shouM be so prepared 
i& to obviate or reduce it to a minimum. This may tistially be done 
Ijy the careful preparation of the foundation to prevent inflow, or by 
."he construction of drains from the interior of the foundation to the 
lower face. 

The construction of a dam with a vertical overfall, unless pro- 
vision is made for the admission of air, will result in the formation 

a partial vacuum below the sheet, and a certain extra strain on 




I ' ^ 




Fig. 363.^Holyoke Dam During Flood. 

istnictiire due to the same. The vertical overfall is also fre- 
llly objectionable, on account of the action of the falling water 
tc bed of the stream immediately adjacent to the dam, and 
foimdation of the dam itself. It is frequently desirable to give 
jwer face of the dam a curved outline, in order to guide the 
Bf smoothly over the dam, and deliver it approximately tang-en- 
the stream bed. The convex surface of the dam should be 
eb form that the water wilh through gravity, adhere to it, 
example of a dam with a curved face is shown by Fig, 361 
is a section of the dam of the Holyoke Water Power Com- 
^uy. Two views of the dam, one during law water (Fig* 362) 
and one with about ten feet of water flowing over the crest (Fig. 




592 



Principles of Construction of Dams. 



363) are also shown. A section of the McCall's Ferry dam, built of 
Cyclopean Concrete (height 53 feet) is shown in Fig. 364 and awe- 
tian of a small Concrete dam at Danville, 111,, is shown in Fig. 365. 
The cur\^e for dams of tliis character should be kept at or above the 




Fir 3S4.— Section of McCall Ferry Dam (Eaag, RecX 



parabolic path that the water wouJd take in a free fall with iht h 
itial horizontal velocity corresponding to the depth of water on iW 
flam. 

From equation 50, page 64, the flow over one foot of crest will 
equal, 

q — vb — m(|)\^2ihl, hence, 
v = m(!)/2iF 

The abscissa of the parabola is x = vt, in which t^ tim« in 
seconds. 



/5teis* BmtM 




^"^i> 






! 




mjs^;,^ 



'^Tifnimnfiffx^' 



I ^ md Dam 



"--C! il 



^\\ 't'Ml 






Fig. 365— Concrete Danir D«nville, HL 



594 



Pnncipltts of Construction of Daou. 



TIic ordinate is, y ^ ^^4 gt*, hence, 

is the equation of tlie pnrabola* 

When a curved face is impracticable or undesirable and the bd 
of the stream, below the dam, is not of suitable material to resist 
the impact of the falling water, some form of apron must be prfr 
vided. Sometimes the dam is divided into steps over which tf.e 
water falls in numerous cascades. Such a dam is shown in Fig. 
366, This is the timber crib dam constructed for the Monuni 




Fig. 367.— Timber Dam at Sewall Falls. (Eng, News» vol. XXS^^ 

Power Company, near Butte, Montana. In this case the cells a^r 
composed of timber, laid alternately in each direction, with a con- 
siderablc space left betw^een them, instead of being built solid 3^ 
in the Kilbourn dam. These cells were filled with broken stone 
and the upstream side of the dam was planked with sheeting i" 
order to make the structure water-tight. When the water wa&| 
admitted behind the dam a portion of the structure was k^^^j 
out of alignment by the crushing of the timbers, at the points 
contacts The amount of this displacement and the cause of tt«fj 
same is quite clearly shown in the cut. 

Fig^ 367 is a section of the Sewall Falls dam, showing a stoi^^ 
method of resisting the impact of the overflow. 

304. Types and Details of Dams. — The types of dams are so ^^^ 
merous, and the details of construction vary so greatly with evi 
locality, that an entire volume w^ould be necessary to adequately 
cover this subject. As the subject is already well covered ip ^"?j 
special treatises and articles, no attempt will be made to discn* 
this subject in the present edition. Numerous references ire p^^] 
to books and articles in which special forms of conslniction s^j 
discussed and described, 
•Turtieaure A UunseW^ * 'Public Water Supplres/* Seclion 446 



LfiteratuTti. 



595 



LlTETRATURm 



PHijfCTPiJEa or coNBTBUCTiaji or hams^ 



TTirneaure and RusBell. Public Water Supplle*. Chaps. 16 to 13. John 

Wiley and Sons, 1901. 
Church, I. P. Mechanics of Engtneerlng. John Wiley and Sons. 1904* 

regmann. Edward. The Design and Gonstniction of DairiB. John Wiley 
and Sons, 1S99. 

L^ffelU James. Construction of Mill Dams. James Leffell and Company . 
Springfield. Ohio. 1831. 

Follet, W. W. Earthen vs. Masonry Dams. Eng. Newg, Jan. 2, 1892» 
et aeq. Eng. Rec. May 14. 1S92. et eeq. 

Hall, F. F. Investigation of the Distribution of Pressure on the Base of 
Dams, Trans. Assn. C. E. of Cornell, 1900. 

Kalght. FranK B, Building an Impounding Dam for Storage Reserroir, 
Mtn^s and Mining. May, 1900» 

Schuyler, J as. Dix. Reservoirs for Irrigation, Water Power and Domes- 
tic Water Supply. New York. Wiley and Sons, 1901. 

Gregory, John H. Stability of Small Dams. Eng. Rec. Sept 21, 1901. 

Fielding, John S. EseeDtial Elements In the Design of Dams. Can, 
E:ngr, Jan. 1M05. 

Wilson. J. S., and Gore, W, Stresses In Dams. Engng. Aug. 4, 1905. 



STABILITY or MASONRY I^AMa 

Coventry, W. B. Design and Stability of Masonry Dams. Proc Inst. 
C, E. ToK S5, p. 2S1. 1SS6. 

Morley, Isaac. On the Determination of the Profile of High Masonry 
Dams. Eng. News, Aug. 11, 1S8S. 

Vischer and Waganer. The Strains !n Curved Masonry Dams, Eng. 
News, Meh. 15, 1890; Sept, 27. 1890. 

Van Buren, John D. Notes on High Masonry Dams. Trans. Am. Soc 
C. E. vol. 34, p. 493. Dec. 1895. 

Pelletlau, M. Profiles for Masonry Dams. Ann. des Ponts et Chausseea. 
Feb. 1, 1897, 

Levy, Maurice. Trapezoidal Formula. Cora p tea Rendus. May 2, 1898, 

Levy, Maurice. The Elastic Equilibrium in a Masonry Dam of Triangu- 
lar Section. Comptes Rendus. July 4, 1898. 

Specifications for a Large Concrete Dam. Eug. Rec. Oct 29. 1898, 

Bainet, M. The Computation of Masonry Dams for Reservoirs. Ann dea 
Ponts et Chaussees. 2 Trlme-stre 1898, 

Baibet M. L. The Conditions of Refli stance of Masonry Dams for Reser- 
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>lllm&n. Geo. L. A Proposed New Type of Masonry Dam. Trans. Ajn. 
Soc. C. E. vol. 49. p. 94. 1902. 




59^ 



Principles of Construction of Dam& 



12, 



DaiBil 



Wlsnen Geo, Y. The Correct Design and StabiUty of Hlgli MasooiXa 
Dams. Eng. News. Oct 1, 1903. 

13. Stability of Masoarj Dams. ^^ngng. Mcb* 31, 1906, 

14. Review of Paper of AtcherlF ^ Pearaoa on StabiUtj of Mbsqutj 

Engr,» Load, Mch. 31. 1905, 

15. Unwin, W. C. Note on the Theory of 0naymmetrlcal Masonry Dtm 

EngGg. Apr. 21. 1905, 
Unwin» W, C, Further Notes on the Theory of Unsymmetrlcal Maaoarr _ 

Dams. Engng. May 12, 190§. ■ 

Tin win. W. C. On the DlstribtJtton of Shearing Stresses In Masonry I>ami^ 

Engng. June 30, 1905, 
Pearson, Karl. On the Stability of Masonry Dams. Engng. fOL M* 

July 14. 1905, 
Wlsner, Geo. Y., and Wheeler, Edgar T, Investigation of Streesea to 

High Masonry Dams of Short Spans. Kng, News. Au^, 10. VM 

20. Pearson, KarL On the Stability of Masonry Dams, Engineeritig, vd. B, 

p. 171. Aug. 11, 1905. 

21. Th« Determination of Pressures on Masonry Dams. Oest. Wochfiisciir, 

f d Oeff, Baudienst. Aug. 19, 1905, 

22. Bletch, S, D. Internal Stresses in Masonry Dams. Sch. of Min» Qr. 

Nov 1905. 

23. Ende, Maxam. Notes on Stresses in Masonry Dams. Engineering. Det 

1905. 



le. 



17. 



18. 



19. 






EARTHEN DAMS, 

1. Fitzgerald^ J. L. Lreakage Throtigb aa Karthen Dam at Lebanau, W-j 

Eng. Rec. May, 1S93, pp. 474^5. 

2. LeConte, L, J. High Earthen Dam for Storage Reservoirs. Proc Am 

W. Wks. Assn.. 1S93, and Eng, Rcc, Sept. 16, 1893. 

3. Fitzgerald, D., and Fteley, A. Construction of Reservoir Emhaakineiiti 

Eng. News. Oct. 26, 1893. pp. 330-1, 

4. Earth Dam of the Honey Lake Valley, California. Eng, News, Mch. 1^- 

1&94. 

5. Earth Dam at New Britain, Conn. Eng. Rec. June 23, 1S94. 

6. Dinirultles with Earth Dams in Great Britain. Eng. Ret. Set. 3, l^^ 

7. Strange, W. L. The Conatmcilon of High Earth Dams. Eng. ^ 

Apr. 15. 1899, 

8. The Limiting Heights of Earth Dams. Eng. Rec. Dec, 7. 190L 

9. A Remarltable Core- wall for an Earth Dam. Eng. Rec. Dec, 21, 1^^^ 

10. Concerning the Design of E]arth Dams and Reservoir f^tmnkmf^^ 

Eng. News, Feb. 20, 1902. j 

11. The Tabeaiid High Earth Dam, near Jackson, Cal. Eng. News. Julj 1^' 

1902. 

12. Baasell. Burr. The San Leandro Eartb Dam of th« Oakland WiW | 

Worlds. Eng, News, Sept 11, 1902. 
IS. The New Earth Dam for Water Works of Santa Fe, N. M. Enf. Ki^"^ < 
Apr, 13, 1903, p, 348. 



iriMiiiiidLi 



Literature 



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598 



Priociples of Constructioa of Dams. 



i 



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27. Flrtb. Charles. Concrete Dams on the Coosa River, Ala Eng. New^ 

Feb. 20. 1896. 
2S. Sayagd, H. N. Repair and Extension of tbe Sweetwater Dam. En$, f^ 

March 12, 1896. 

29. Tha Cold Spring, N. Y.. Concrete Dam. Eng, Rac. July 11, 1891 

30. HcPMCheid and Cheminiz Water Works. Eng., Lend. Julv SI, 1S98, 

31. New Arched Dam at Nashua, N. H. Eng, Rec. Aug. 8. 1S9S. 
S2. Dahl, H. M. T A New Dam at Minneapolis. Eng'a Year Book UsJt oJ 

Minn.. 1897. 




Literature. 599 

33. The Proposed Steel-Faced Concrete Arch Dam. Ogden, Utah. Eng. Rec. 

Mch. 6, 1897. 

34. Thompson, Sanford B. The New Holyoke Water Power Dam. Eng. 

News. May 13, 1897. 

35. Homey, Odns C. Ck)ncrete Water Power Dam at Rock Island Arsenal. 

Jonr. W. Soc. Engs. June, 1897. 

36. Schnyler, James D. The Construction of the Hemet Dam. Jour. Assn. 

ETngng. Socs. Sept. 1897. 

37. Schuyler, James D. The Hemet Irrigating Dam. Sci. Am. Sept 25. 

1897. 

38. The Muchkundi Dam. Engr. Lond. Oct 22, 1897. 

39. The Hemet Dam. Eng. News. March 24, 1898. 

40. Richter, Irving. An Unusual Small Masonry Dam. Eng. Rec. Nov. 26,. 

1898. 

41. Rafter, G. W., Greenlach, W., Horton, R. E. The Indian River Dam. 

Eng. News. May 8, 1899. 

42. Crosby, W. O. Geology of the Wachusett Dam and Aqueduct Tunnel. 

Tech. Quar. June, 1899. 

43. The New Masonry Dam at Holyoke. Eng. Rec. July 22, 1899. 

44. Gould, E. S. Earth Backing for Masonry Dams. Eng. Rec. Dec. 23, 

1899. 

45. The Bear Valley Dam as an Arch. San Bernardino Co., Cal. Techno- 

graph No. 14, 1899-1900. 

46. The Tariffvllle Plant Plans of Hartford Elec. Light Company. Eng. Rec. 

Mch. 24, 1900. 

47. The New Water Power of the Hartford Electric Light Co. Am. Electri- 

cian. Mch. 1900. 

48. Flinn, Alfred D. The Wachusett Dam. Eng. News. Sept 13, 1900. 

49. The Wachusett Dam. Eng. Rec. Sept 8, 1900. 

50. A Concrete* Power Dam at Middle Falls, N. Y. Eng. Rec. Oct. 4 1900. 

51. Stewart, J. A. Building of the Great Wachusett Dam. Sci. Am. Sup. 

Dec. 15, 1900. 
62. The Dam ft Power Station of The Hudson River Power Company. Eng. 
Rec. Mar. 8. 1902. 

53. Heaman, J. A. Description of a Dam and Accompanying Work Built for 

the Water Commissioners. Can. Soc. of Civ. Engrs. Apr. 24, 
1902. 

54. A Concrete Dam Near London, Ontario. Eng. Rec. July 26, 1902. 

55. Frechl, H. Construction of the Lauchenesee Dam. Eng. Rec. Aug. 30, 

1902. 

56. The Spier's Falls Dam of The Hudson River Water Power Company. 

ETng. News. June 18, 1903. 

57. Morton, Walter Scott A New Water Power Development at New Mil- 

ford, Conn. Eng. Rec. Feb. 13 and 20, 1904. 

58. Harrison, Chas. L., and Woodard, S. H. Lake Cheesman Dam and Re^ 

ervoir. Proc. Am. Soc. C. E. Aug. 1904. 

59. Galliot, M. Reinforcement of the Grosbois Dam. Ann. des Ponts et 

Chaussees, 1905. 



Boo 



Principles of Construction o! Dams, 



€0- *f!ie Rooieyelt Masonry Dam on Salt River. Arizona. Eng. News. Jui. 

12. 1905, 
6L A Quickly Erected Eel n forced Concrete Dam at Fen el on Fafla, Out ^H 

News. Feb. 9. 1905* 

62. A Concrete Dam on a Pile Foundatioii at St. John '8 Lake, Ijans Ulaai 

N, y, Eng. News. Feb, 9. 1905, 

63, Qnarinl, Emile. Barosaa Dam, Southern Australia. ScL Am. AprU i 

1905. 
HoHow Reinforced Concrete Dam at Sebuyldrrtlle, K. T. Bn^. Newa. 

April 27. 1905. 
Blodgett, Geo. W. The Wachuaett Dam of the Metropolitan Water 

WorkB. R. R. Gai,, vol. 39, p. 100. Aug, 4. l%m. 
Dams for the New Plant of the United Sttoe Machinery Comiiaiiy, Be^ 

erly, Mass. Eng. Rec. Sept 2. 1905, 
Shedd, Geo. 0. The Garvin 'i Falls Dam, Canal and Hydro-Eleetrtc Ptaut 

Jour. Aesh. Eng. Soc, OcL 1905. 
G<iwes, Chas. S, Chaagcs at the New Croton Dam, Proc, Am, Soe, C E- 

Mch. 1906. 
69, The Pedlar River Concrete Block Dam. Lynchburr W. Wks. Eng. Rk. 

May 13. 1906. 
TO. The Streeses on Masonry Dams. Editorial Review of Paper by ProL 

Carl Pearson. Engineering. London, September, 1907. 
71. The McCall'a Ferry HydiauUc Electric Power Plant. Eng* News, 

tembcr 12. 1907, 



I 



64 



65 



66. 



67. 



68, 



TIKBiS DiLMS. 



S€|h I 



L Parker. M, S. Biack Eagl© Falls Dam at Great Falla. Mont Tnni 

Am. Soc. C, E. July. 1 890. vol, 27, pp. 56-59. Eng. Rec Oct i 

1892. p, 295. 
2. Sewell Falls Dam Across Merrlmac River, near Concord » N, H. Eofi 

News. April 19, 1894. 
Z. Parsons, G. W. CI o slug the Timber ft Stone Dam at Bangor, Ma Eof 

News. July 26. 18S4. 

4. Brown. Robert Oilman. Additions to the Power Plant of the Stftflda^*^ 

Consolidated Mining Company. Trans, Am. Inst Mining Eur*. 
Sept. 1896. 

5, Ripley, Theron M. The Canyon Ferry Dam, Canyon Ferry » Mont Joar. 

Assn. Engng. Soc. May, 189S. 

6. The Butte. Montana, Power Plant Eng. Rec. Mch, 5. 1898. 

7, Carrol t ETugene. Construction of a Crib Dam for Butte City Water O^- 

Butte, Montana. Jour. Absu, Engng. Soc. April. 1899, 
S, The Reieonatructed Canyon Ferry Dam, near Helena, Montana. Eni 

News. Apr, 26. 1900. 
9, A l^rge Crtb Dam. Butte. Mont. Eng. Rec. Feb. 3, 1900. 
10. Harner. Jos H. The Reconstruction of Big Hole Dam, Big Hole. MW^ 

tana, Jour. Assn. of Engng. Soc. Apr. 1900 




Literature. 6oi 

11. Tower, G. W. Timber Dam at Outlet of Chesunoook Lake, Penobscot 

River. Eng. News. Sept. 1, 1904. 

12. Woermann, J. W. A Low Crib Dam Across the Rock River 

STEEL DAJiS. 

1. Fielding, John S. The Use of Steel In the Construction of Dams. Can. 

Arch. Aug. 1897. 

2. Steel Weir, Ash Fork, Arizona. Eng. Rec. Apr. 9, 1898. 

3. Steel Dam at Ash Fork, Arizona. Eng. News.. May 12, 1898. 

4. Fielding, John S. Proposed Design for a Steel and Concrete Dam. Eng. 

News. Nov. 16, 1899. 

5. Bainbridge, F. H. Struc ural Steel Dams. Jour. West. Soc. Enpr. 1905. 

6. The Hauser Lake Steel Dam in the Missouri River Near lledena, Mont 

Eng. New. Nov. 14, 1907. 

7. Wheeler, J. C. A Collapsibe Steel Dam Crest. ETng. News. October 8. 

1907. 

BEINFOBCED CONCRETE DAMS. 

1. A Large Reinforced Concrete Dam at Ellsworth, Maine. Eng, News. 

May, 1907. 

2. A Hollow Reinforced Concrete Dam at Theresa, New York. ETng. News, 

Nov. 5, 1903. 

3. Reinforced Concrete Dam at Schuylerville, New York. Eng. News, April 

27, 1905. 

4. A Concrete Steel Dam at Danville, Kentucky. Eng. Rec. Dec. 3, 1904. 

5. Reinforced Concrete Dam at Fenelon Falls, Ontario. Eng. News, Feb. 9» 

1905, 

DAM FAILURES. 

1. Washout at the Pecos Dam. Eng. Rec. Aug. 26. 1893. 

2. Failure of the Bouzey Reservoir Dam. Lon. Engr., May 3, 1895, p. 588; 

Eng. News, May 9, 1895, p. 312; Lon. Engr., May 31, 1895, p. 
883; Eng. News, May 23, 1895, p. 332. 

3. Catastrophe at Lima, Montana. Irrigation Age, July, 1894. 

4. Rickey, J. U. Failure of Dam at Minneapolis, Due to Previous Weaken* 

ing Through Ice Pressure. Eng. News, May 11, 1899. 

5. Failure of Masonry Dams. Annales des Fonts et Chaussees, vol. 7, No. 7,. 

pp. 77-89 (1895). 

6. The Johnstown Disaster. Eng. News, June 18, 1899. 

7. Recent Events at the Castlewood Dam, Castlewood, Colo. Eng. Rec 

May 19, 1900. 

8. The Failure of Two Earth Dams at Providence, R. I. Eng. News, Mch. 

12, 1901. 
3. Destruction of Datns In the South. Eng. Rec. Jan. 11, 1902. 
1^0. The Failure of the Dam of the Columbus Power Company at Columbus^ 

Oa. Eng. Nef^'S. Jan. 23, 1902. 



6o2 Principles of Construction of Dams. 

11. Failure of the Lower Tallassee Dam at Tallassee, La. Eng. News. Feb. 

13, 1902. 

12. Johnson, Robert L. Some Thoughts Suggested by the Recent Failure 

of Dams in the South. Eng. News, Mch 20, 1902. 

13. Hill, W. R. A List of Failures of American Dams. Eng. Rec. Sept 27, 

1902. 

14. The Break in the Utica Reservoir. Eng. Rec. Sept 27, 1902. 

15. Whited, Willis. The Failure of the Oakford Park and Fort Pitt Dam. 

Eng. News, July 23, 1903. 

16. Robinson, H. F. Construction, Repairs and Subsequent Partial Destruc- 

tion of Arizona Canal Dam. Eng. News, Apr. 27, 1905. 

17. Murphy, E. C. Failure of Lake Avalon Dam, near Carlsbad, N. H. Enf. 

News, July 6, 1905. 



CHAPTER XXV. 

APPENDAGES TO DAMS, 

305, MDvsiBle Dams, — The height of a dam is limited in the mati- 
ler hereinbefore described. It will be noted that the limit is that 

iposed by high water conditions and that, as a rule, the water sur- 
icc during low stages could be raised to a considerable amount 
nthout interference with the riparian owners, if at the same time 
lood conditions could be provided for. In order to provide such 

>nditions, movable dams are sometimes constructed which will 

*rmit of raising or lowering all or a part of the structure as the 





n^ 36S* — V. B, Movable Dam on PUe Foundation, McMeclien, W. Vi. (l?kif, 
Newa, YoL 54, page lOOJ 



stage of the water requires. These flexible portions of the dam 
may consist of a gate or series of gates which can be raised or 
lowered. Sometimes a considerable portion of the dam is made 
flexible by the construction of a bear trap leaf, which is usually 
raised and lowered by hydraulic pressure, and by means of which 
the head of water can be readily and rapidly controlled. Sometimes 





Movable Dams. 



605 



entire dam is made movable by the use of Cbanoine wickets 
^«e Fig^, 368) and similar types of dams, a part of which may be 
^novable while other parts are folded down on the bed of the 
■r-eam, allowing the flood waters to pass over them. Most of such 




Fig, 370,— Tainter Gates for Morria Plant, Ecanomy Light and Power Co. 

onstructions are expensive and are used most largely on govem- 
nent works for the control of rivers for navigation purposes. 

The objection to movable dams for water power purposes is 
hat the reduction in the elevation of the head water by their use 
ommonly su reduces or destroys the head that the continuity of the 




6o6 



Appendages to Dam 



power output is intemipted. The same objection also applies 10 
any gate, flash board or other device designed to reduce tlie head. 
Such reduction is usually made during conditions of flow undfr 
which the natural head that would obtain is already at a minimum, 
306. Flood* Gates. — Flood gates are quite commonly used h 
water power dams to control or modify extreme flood hetgbti 
These gates are commonly designed to be raised so as to perniitj 
the escape of the water underneath them. The tainter gate,] 




Fig. 371^— Hoist for Tainter Gates of Northern Hydro Electric Power Odl 



some of its modifications, is perhaps most widely used for this pur- 
pose. Fig, 369 shows a plan, elevation and section of a tainlj 
g^te, designed by L, L. Wheeler* resident engineer of the 
and Mississippi Canal, for the U. S, Government dam at Stef^ 
Illinois. This is one of a series of tainter gates designed 
flood control of the Rock River at that point. The gates af 
ated by an overhead hoist which can be moved from gate (ril 
when it is desired to manipulate them, 

Fi^' 370 is a section of one of six gates designed by the wild 
for the Morris plant of the Economy Light and Power Conipani 



FloodGatea* 



607 




Fig. 372,— Tainter Gates at Upper U, S. Gov. Dam, Appleton, Wis. 




Fig, 373,— Ta!Dter Gatea at Lower U. S. Gov. Dam, Appleion, Wis. 




Flashboards. 



609 



These gates are operated by a movable hoist, similar to Fig, 371, 
irhich travels on a track on the brige above, 

F>&s- 372 and 373 are views of the steel tainter gates constntcted 
n the upper and lower U, S. Government dams across the Fox 
^tvcr at Appleton^ Wisconsin. 

In the dam of the Southern Wisconsin Power Company at Kil- 
loum, Wisconsin, the rise of the flood water is so great (about 16 
cet) that it was found impracticable to const met lift gates to re- 
luce the flood heights. In this case the writer has divided the crest. 




fig. 375. — Flush Boards and Supporta, Rock ford Water Powjipr Co, 



by piers, into twelve sctions. Between each two piers a twenty- 
five foot gate is placed (see Fig* 374) which can be lowered into the 
dam six feet, thus reducing the extreme flood height by that amount. 
These gates are of steel and weigh about seven tons each. They 
may be operated by an electric motor or may be manipulated by 
hand, should occasion require. 

307. Flashboards. — ^Tbe control of limited variations in head is 
commonly accomplished by means of flash-boards wliich are widely 

ed for this purpose. The simplest form otf flash -board consists 




6io 



Appendages to Divms, 



of a line of boards placed on the crest of the dam (see Fig. 3751 
usually held in place by iron pins to which the boards arc com- 
monly attached by staples* The object of Rash-boards is prind^ 
pally to afford a certain pondage to carty the surplus water itm 
the time of minimum use of power to the time of maximum detnani 
Incidentally, the head is raised and the power is also increased in 
this way. The supports of the flashboards should be so arranged 
that they will withstand only a comparatiyelly low head of water 
flowing over the boards, and will be carried away if a sudden 




m^- 



Fig. 376. — Automatic Drop-Shutter for Betiva Dam, India.. (Bd£. Sttt 

June it 1903J 



flood should raise the head materially above a safe clevatioa If 
the boards are so supported as to withstand the discharge of hetvj 
floods, they will form a permanent portion of the dam and increase 
its fixed elevation to such an extent as to create damage which their 
use is supposed to avoid. Sometimes the pins supporting thCj 
boards are made so light that they must be held in position bj ia 
clined braces. These braces are sometimes supplied with stt 
eye*boUs through which is passed a cable. A large steel washc 
is attached at one end and a winding drum at the other* (Sec Fij 
375), Commonly, if a flood is anticipated, the boards are removi 
and stored for future use. If, however, a sudden flood should arii 
the inclined braces are removed by winding up the cable an 
the pressure on the flash-boards bends the pins and the hosLfi^ 
are washed away. The expense involved by the loss of flash^boards 



Head Gates and Head Gale Hoists, 



eii 



is not excessive as one set will commonly take care of the entire 
summer low water period. The expense involved in their use 1% 
:herefore only the cost of one set of flash-boards per year. 

Sometimes the flash-boards constitute a permanent bt!t adjust- 
ible part of the dam and arc lowered automatically during stages 
>f high water* (See Fig. 376). On some dams, especially at 
jvaste weirs of canals and reservoirs where the fliictiiations in 
leight are inconsiderable* the dam may be provided with a foot 
>ridge which makes the whole crest of the dam accessible at all 
imes and from which the flash -boards can be readily adjusted. 
rhis plan is used on the dam across the Chippewa River at Eau 




Fig, 377,— Adjustable Flaah Boards at Eau Claire, Wii. 

Claire, although this river is subject to high floods. (See Fig. 377). 
Ordinarily, on rivers stibject to such conditions, this type of con- 
struction is impracticable* 

In some dams, instead of gutes or flash-boards, vertical stop 
planks or needles arc used. These consist of planks or squared 
timbers that are lowered vertically into position, stopping off the 
opening partially or wholly, as desired. They are commonly sup- 
ported by a shoulder at the bottom of the opening and one or more 
cross beams above. 

308* Head Gates and Head Gate Hoists.^-It is usually desirable 
to control the water at the inlets to the headrace by the use of gates 

:iich may be closed in emergencies or for the purpose of making 




6l2 



Appendages to Dams. 

I 



fr 




6 14 



Appeodages to Dain^ 



necessary repairs or modifications in the race^^ay through which 
the water is diverted to the plant. In northern rivers it is also 
found desirable to prevent the entrance of ice into the raccwij 
either by the construction of a Boating or fixed boocn In front oi the 
gates or by constructing a system of snbmerged arches cither b 
front of, or as a part of, the gateways. By means of snch constnjc- 
tioo the floating tee or other floating material may be diYCfled froio 
tlie raceway and passed over the sptliway of the dam^ 

The head gates must be sufficiently substantial to allow the net 
to be emptied under ordinary conciitions of water and to pnsted 
the race^vay under flood conditions. 

Fig. 378 shows an elevation of the head gates, designed by ^ 
writer for the power plant at Constantine, Michigan* These ire 
shown in detail "by Fig. 379. A rear view of these gates from the 
race side is also shown in Fig. 38a These gates are double wooden 
gates with concrete gateways and are arched over between the 
piers so as to permit the passage of men and teams. These gata 
are designed to pass about ^jooo cubic feet per second. 

Fig. 3S1 shows a set of double wooden gates, the posts and braca 
of which are made of structural steel designed by the writer f<K tke 
power plant of Mr. Wait Talcott, at Rockford, Illinois, 

In the Cbnstantine g^tes the gate mechanism is geared for fair!? 
rapid operadoii by two meik The Rockiord gate apparatus is very 
simple, the gate being handled with a capstan bar by a siogk m»st 
but at a much slower ^»eed. 

Ftg. 382 sho¥rs the movable head gate hoist designed by die 
writer for the c^ietatiOQ of the head gates at the Kifbooni pbnt of 
tlte Somthem Wisconsin Power Company. 

J09. Fi^Ways^'^In almost eTcry state fishways are re«j 
law in any dam constmcted om natural waterways. The^ fis! 
imys smst be so arranged as to permit the free passage of fish tif ^ 
the stiemm, 

Fif * 3S3 shows a concrete fishway bnilt by the writer in ccw^ 
necUoo with the og<ee conocte dam constructed across the Vc 
million Riv^ at DAnviIle« ItEnois. Fig. 384 is a fishway deslgne 
by Mr, L. L. Wlieeler and cottstraded in the dam at Sterling* '< 
aojs. The Sterling dam is a thnb^ crib dam and the fishwty ! 
cmSElriicted of timber. Fig. 385 shows the type of Bshway 
iMftied by the Fidi Comwis^oa of the State of Wi 
onltnarilT used tn tliat state. 



6i6 



Appendages to Dams. 





Head Gates and Head Gate Hoists, 





Fig. 3S2.-Head Gatis Hoiet, Kilbourn, WIb. tScuthern Wisconsin Power Ca) 

The purpose of these fish ways is to afford a gradual in c line 
through which a continuous stream of water of comparatively low 
velocity shall flow and against which the fish may readily swim. 
Both the inlet and outlet should be below low-water and the out- 
let should be in such a position that the fish, when they ascend the 
stream and reach the dam, in passing from one side to the other in 
searching for a passage, are naturally led to the point where the 




6i8 



Appendajjes to Dams 




Fishwayi* 



6x9 




Fig. SS4,— Timber Flsliway In Dam at Sterling. IlL (Eng. Newe.) 




Fig. 383.--FiBhway of Fish Commiaalon, State of WiBC^onslB. 



620 



Appendages to Dams« 



flowing water is encountered. The slope of these Ushwars sbodd 
not be steeper than one vertical to four horizontal, and the water 
should be so deflected that the velocity will be reduced as low i5 
possible. A fish way should be entirely automatic and free iituE 
all regulating devices. It is usually desirable for the opening h 



Si-£¥B*M 



SPtLLWA r SECnOH 




Log- Ways- 



621 



Jio. Log- Ways, — The free navigation of streams for legging 

mrposes is provided by law in most states and it is therefore neces- 

iry where logging is practiced to provide ready means for their 

issage over or through the dam. This is accotnplishcd in the 




Fir. 317-^ — Log Way at Lower Danij MioneaiwJIflp MtniL 

Kilbourn dam (see Fig. 374) by the lowering of any one of the 
flood gates. 

Fig. 386 shows a plan and section of the log-sluice constructed in 
the Chesuncook timber dam on the Penobscot Riven A section of 
the spillway of the dam is also shown in the same figure. 

Fig. 3S7 is a view of the logway in the lower dam at Minneapolis. 
This sluice is only six or eight feet in width, and the depth and 
quantity of water flowing is controlled by a bear trap leaf, 
9ti 



63a Appendages to Dams. 

In most cases, to avoid an excessive waste of water, it is desk* 
able to build the logway as narrow as possible. Under such ^ 
tions it becomes necessary to guide the logs into the sluice by 1 
ber booms which, leaving the sluice at a low angle, are strung i^ 
stream to such points that the logs in floating down stream M 
enter between them and be guided to the sluice opening* 



UTERATUlia 

1C07ASLS DAM3, FI.ASHB0ABD3« KTO^ 

1, Harcourt, Li V, FUed and Movable WeirB, Proc, Ins. C. E. VoL fii 

p. 24. Jan. ISSO. 

2, Cbittenden. Hiram ftl American Types of Movable D&ms. Eng, N«n 

Feb. 7, 1S95. VoL 33, p, 81 
B. StlckneTp Amos. Lifting Dam. Jour. Abbu. Eug. Soc Vol. 16, p. 33i 
June, 1896. 

4. Tbomas, B. F. A Design for a Movable Dam. Jour. Assn. E^g: Sdc» 

VoL 16» p. 260, June. 1856. 

5. Chittenden, H. M. Modified Drum Weir. Jour. Abso. Eng. Soc. Vd 

IS, p. 249. June, 1S9G. 

6. Powell, Archibald 0. Movable Dams, Sluice and Lock Gates of Ibe Bei^ 

Trap Type. Jour. Aaao, Eng. Soc. VoL 10, p. 177. Jaae, nU. 

7. Marshall, W, L. Marshali*s Bear-Trap Dams, Jour. Assn. Eag. Sot 

Vol. 16, p. 21S. June, 1896, 
S. Jonea, W. A. Bear-Trap Weirs. Jour. Assn. Eng, Soc. Vol. Ifi, p. 2^ 

June, 1896. 
9. Jolinson, Archibald. Bear-Trap Gates in the Navigable Pass, Sandy Uke 

Reservoir Dam, Minnesota. Jour. Asan. of Eng. Soc, Vol li 

p. 210. June, 1896. 
to. Martin, Wm. Bear-Trap Gate lo Davis Island Dam, Ohio RiTer. Jour, 

Asso. Bug. Soc. Vol. 16, p. 208. June. 1S96. 

11. Movable Dama on the Great Kanawba River. Eng. News, ttdL S6, p. i2i 

Dec. 31, 1896. 

12. Needle Dams. Ann, dea Fonts et Chaussces. Part 11. IS 97* 

13. Bear-Trap Dam. Chicago Drainage Canal, B. VL Gaz. Feb. 12, 1897. 

14. The Use oC Rolling Shutters tn Movable Dams. Genie Civil. May I. Wl 
IB. LArmlnie, J. C. Falling Shutters, Godavery, Anient* Ind. Eng. De: 

18, 1897. 

16. Thomas, B. F. Movable Dams. Tra^s. Am. Soc. C, E. Vol. 39, p. Ul 

Mar 1S98. 

17. Bear-.Trap Dam for Regulat[ng Works, Chicago Drainage Canal. Eag- 

News. Mar, 24, 1898. 

15. The Movable Dam on the Big Sandy River. Q^nta CirU. May II, ISftl 
19. Marshall Automatic Movable Dam. Eng, News. May 29, 1S9S. 



w. 



Literature. 623 

). The Management of Non-parallel Motion and Deficient Operating Head 

in Bear-Trap Dams by Auxiliary ConBtructions. Bng. News. 

May 26, 1898. 
L New United States Qovernment Needle Dam at Louisa, Kentucky, on the 

Big Sandy River. Eng. News, vol. 40, p. 2. July 7, 1898. 
I. The Chittenden Drum Dam. Sng. Rec. Vol. 40, p. 356. Sept. 16, 1899. 
I. Claise, M. The Resistance of Dam Framing. Ann des Fonts et Chaus- 

sees. 4 Trimestre, 1899. 
I. A New Automatic Movable Dam. EIng. Rec. Vol. 45, p. 222. March 8, 

1902. 
5. Reconstruction of the LAke Winniblgoshish Dam. Eng. Rec. Vol. 46, 

p. 250. Sept. 13, 1902. 
C. Hilgard, K. EL Roller Dams. Schwelzerlsche Bauzoitung. Bd. 43 8. 

65 u. 86. Feb. 6-13, 1904. 
.7. ^oechlin, Rene. Large Rolling Dams. Genie Civil, Feb. 27, 1904. 
!8. Guarini, Emile. Rolling Dams at Schwelnfurt, Bavaria. Eng. News, 

vol. 53, p. 57. Jan. 19, 1905. 
M. Walker, Gilbert S. Pile Foundations for Movable Dam at McMechen, 

W. Va. Eng. News, vol. 54, p. 100. July 27, 1905. 
10. Movable Dam and Lock of The Rice Irrigation and Improvement Assoc., 

Mermentau River, La. Eng. News, vol. 54, p. 321. Sept 28, 1905. 
|1 Movable Crest Dams at the Water Power Development of the Chicago 

Drainage Canal. Eng. Rec. Vol. 56, p. 194. 
H Johnston, C. T. Masonry and Steel Head Gates of the Grand Valley Ir- 
rigation Canal. Engineering News, VoL 50, p. 141. 
M. Hanna, F. W. Electrically Operated Gates for the Roosevelt Dam. Eng. 

News, vol. 57, p. 586. 
•i Qaona, F. W. Hydraulic Gates for Drainage Tunnel, Kern River Plant 

Eng. News, vol. 51, p. 326. 
US. Leighton, M. O. High Pressure Sluice Gates. Jour. West. Soc. Eng. 

Vol. II, p. 381. 
^ Gillette, H. P. The Rudder Boom. Eng. News, Vol. 47, p. 473. 

nSHWATS. 

^ Gerhardt, Paul. Flschwege and Flschteiche. Verlag Von Wilhelm En- 

gelmann. Leipzig, 1904. 
2- Leslie, Alexander. Salmon Ladders in Scotland. Institute of C. B. Vol. 

89, p. 304. 



CHAPTER XXVL 

PONDAGE AND STORAGE^ 

311. Effect of Pondage on Power. — ^The terms "Pondage" and 
"Storage" are quite similar in meaning, both having reference to 
the impounding of water for future use. The term pondage us- 
ually refers to the smaller ponds which permit of the impounding 
of the night flow for use during the working hours of day. Stor- 
age, on the other hand, is usually applied to the larger impounding 
reservoirs that enable a sufficient quantity of water to be stwed 
to carry the plant, to some extent at least, through the dry season 
of the year. Between these limits every variation in capacity is 
of course possible. 

In Chapter IV, Section 54, the effect of pondage on the power 
of a stream is briefly outlined and illustrated by hydrographs 
shown in Figs. 41 and 42. The pondage illustrated by these dia- 
grams is sufficient to store the entire flow of the river during the 
parts of the day when the power is not in use and reserve it for 
those hours of the day when the power is needed. Such a condi- 
tion can frequently be realized for the low flows during the dry 
seasons, but the capacity is seldom sufficient to store the larger 
Hows, and if sufficient should be investigated in a different manner 
to be discussed later. These hydrographs (Fig^. 41 and 42) 
should therefore be examined with these points in view. 

In many water power installations practically no pondage is pos- 
sible and the power of the stream must be utilized as it flows or 
otherwise it will be wasted. On continuous service, such as i** 
sometimes required by cotton factories, paper mills, and elec